[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":-5,"_10":11,"_12":13,"_14":15},"actionData","errors","root",{"_26630":26631,"_26632":26633,"_26634":26635,"_26636":42,"_26637":26638,"_26639":42,"_26640":26641,"_26642":26643,"_26644":40,"_26645":26646,"_26647":-5,"_26648":-5,"_26649":-5,"_26650":-5,"_26651":-5,"_26652":-5,"_26653":26654,"_26655":26656,"_26657":42,"_26658":-5,"_112":42},"routes/__learning-environment",{"_19993":20378,"_20379":20380,"_20381":20382,"_20383":20384,"_112":42},"routes/__learning-environment/course","routes/__learning-environment/course/$courseSlug",{"_79":19985,"_19986":19987,"_19988":42,"_112":42},"routes/__learning-environment/course/$courseSlug/topic.$topicSlug.$level.$gradeOrExam",{"_79":80,"_81":82,"_83":84,"_85":86,"_87":88,"_89":90,"_91":92,"_93":94,"_95":96,"_97":44,"_98":99,"_100":101,"_102":103,"_104":105,"_106":107,"_108":42,"_109":110,"_111":-5,"_112":42},"routes/__learning-environment/course/$courseSlug/topic.$topicSlug.$level.$gradeOrExam/faq",{"_16":17,"_18":19,"_20":21},"topicTitle","De grafiek van een wortelfunctie","questions",[22,23,24,25,26],"backButtonHref","/course/wiskunde-b/topic/de-grafiek-van-een-wortelfunctie/vwo/5",{"_27":71,"_29":72,"_31":73,"_33":74,"_35":75,"_37":76,"_39":40,"_41":42,"_43":44,"_45":44,"_46":77,"_48":78},{"_27":64,"_29":65,"_31":66,"_33":67,"_35":66,"_37":68,"_39":40,"_41":42,"_43":44,"_45":44,"_46":69,"_48":70},{"_27":57,"_29":58,"_31":59,"_33":60,"_35":59,"_37":61,"_39":40,"_41":42,"_43":44,"_45":44,"_46":62,"_48":63},{"_27":50,"_29":51,"_31":52,"_33":53,"_35":52,"_37":54,"_39":40,"_41":42,"_43":44,"_45":44,"_46":55,"_48":56},{"_27":28,"_29":30,"_31":32,"_33":34,"_35":36,"_37":38,"_39":40,"_41":42,"_43":44,"_45":44,"_46":47,"_48":49},"uuid","408bbb42-eea1-4490-8ab2-1c077c68972d","slug","bereik-wortelfunctie-pijl-links-domein-niet","question","Waarom heeft het bereik van een wortelfunctie een pijl naar links en het domein niet?","cleanedQuestion","Waarom bereik wortelfunctie pijl links domein","detailedQuestion","Ik ben bezig met wortelfuncties en ik snap niet goed waarom de notatie voor het bereik soms een 'pijl naar links' heeft, wat betekent dat de y-waarden kleiner worden, terwijl de notatie voor het domein dit nooit heeft. Ik zie in de grafiek soms wel dat de lijn van het domein ook naar beneden loopt, dus waarom wordt dit dan niet met een 'pijl naar links' aangegeven voor het domein?","answer","Het domein van een wortelfunctie bestaat uit alle mogelijke x-waarden die de functie kan aannemen. Voor een standaard wortelfunctie begint de grafiek bij een randpunt en loopt deze altijd naar rechts. Dit betekent dat de x-waarden altijd groter zijn dan of gelijk zijn aan de x-coördinaat van het randpunt. Daarom wordt het domein meestal genoteerd als $x \\ge \\text{x-coördinaat randpunt}$, wat aangeeft dat de waarden naar rechts (groter) gaan en er geen 'pijl naar links' (kleiner worden) in de notatie voorkomt.\n\nHet bereik van een wortelfunctie bestaat uit alle mogelijke y-waarden. Ook hier start je bij het randpunt. De richting van de grafiek vanaf het randpunt is afhankelijk van de functie zelf. Als de wortelfunctie vermenigvuldigd wordt met een negatief getal (bijvoorbeeld bij $g(x) = -2\\sqrt{x+4} + 6$), wordt de grafiek verticaal gespiegeld. Dit betekent dat de grafiek vanaf het randpunt naar beneden loopt. In dat geval worden de y-waarden kleiner of gelijk aan de y-coördinaat van het randpunt. De 'pijl naar links' in de notatie voor het bereik verwijst naar deze situatie, waarbij de y-waarden dalen (kleiner worden), bijvoorbeeld $y \\le \\text{y-coördinaat randpunt}$.\n\nHet is belangrijk om te onthouden dat de richting van de x-waarden (domein) en de y-waarden (bereik) los van elkaar staan. Zelfs als de grafiek visueel naar beneden loopt (wat invloed heeft op het bereik), blijven de x-waarden (domein) altijd groter of gelijk aan de x-coördinaat van het randpunt, wat betekent dat het domein altijd naar rechts uitstrekt.","isConcept",false,"isSynced",true,"likeCount",0,"dislikeCount","createdAt",["D",1758202024439],"updatedAt",["D",1758202024634],"4785f974-7379-423e-a6b1-61be92bfee83","hoe-bepaal-je-het-domein-van-een-wortelfunctie","Hoe bepaal je het domein van een wortelfunctie?","bepaal domein wortelfunctie","Het domein van een wortelfunctie omvat alle mogelijke waarden voor $x$ waarvoor de functie een reëel getal als uitkomst heeft. De belangrijkste regel hierbij is dat de uitdrukking onder een wortelteken nooit negatief mag zijn.\n\nOm het domein te bepalen, stel je de uitdrukking onder de wortel groter dan of gelijk aan nul ($\\ge 0$).\n\n**Voorbeeld:**\nNeem de functie $Y = \\sqrt{X-5}$.\nOm te zorgen dat $Y$ een reëel getal is, moet de uitdrukking onder de wortel, dus $X-5$, groter dan of gelijk zijn aan nul:\n$X-5 \\ge 0$\n$X \\ge 5$\n\nHet domein van deze functie is dus $X \\ge 5$. Dit betekent dat $X$ elke waarde van 5 of hoger mag aannemen. Als $X$ bijvoorbeeld 14 is, dan is $Y = \\sqrt{14-5} = \\sqrt{9} = 3$. Als $X$ kleiner is dan 5, bijvoorbeeld 4, dan zou je $\\sqrt{4-5} = \\sqrt{-1}$ krijgen, wat geen reëel getal is.\n\nHoewel er in de wiskunde ook complexe getallen bestaan (waarbij de wortel van een negatief getal wel gedefinieerd is, bijvoorbeeld $\\sqrt{-1} = i$), focussen we ons op de middelbare school meestal op reële getallen. Voor reële getallen geldt dus altijd: de uitdrukking onder de wortel moet $\\ge 0$ zijn.",["D",1774826503576],["D",1774826503934],"6960c63e-00ef-4cfc-b74a-8422f0f39c4b","wat-is-het-bereik-van-een-wortelfunctie","Wat is het bereik van een wortelfunctie?","bereik wortelfunctie","Het bereik van een wortelfunctie zijn alle mogelijke uitkomsten (functiewaarden) die de functie kan produceren. Voor een standaard wortelfunctie, zoals $f(x) = \\sqrt{\\text{uitdrukking}}$, geldt dat de uitkomst van een wortel per definitie altijd $0$ of groter is. Een wortel kan nooit een negatief getal als resultaat hebben in de reële getallen.\n\nDit betekent dat de functiewaarden, oftewel het bereik, van een wortelfunctie altijd groter dan of gelijk aan $0$ zijn. We noteren dit als $f(x) \\ge 0$.\n\n**Voorbeeld:**\nNeem de functie $k(a) = \\sqrt{a+2}$.\n1. **Domein (mogelijke waarden voor $a$):** De uitdrukking onder de wortel, $a+2$, moet altijd groter dan of gelijk zijn aan $0$. Dit betekent $a+2 \\ge 0$, dus $a \\ge -2$. Dit zijn de waarden die je voor $a$ mag invullen.\n2. **Bereik (mogelijke uitkomsten van $k(a)$):** Als je een geldige waarde voor $a$ invult (bijvoorbeeld $a=-1$, dan is $a+2 = 1$), dan is de uitkomst van de wortel ($\\sqrt{1} = 1$) altijd $0$ of groter.\n * Als $a=-2$, dan is $k(-2) = \\sqrt{-2+2} = \\sqrt{0} = 0$.\n * Als $a=-1$, dan is $k(-1) = \\sqrt{-1+2} = \\sqrt{1} = 1$.\n * Als $a=2$, dan is $k(2) = \\sqrt{2+2} = \\sqrt{4} = 2$.\nIn alle gevallen is de uitkomst $k(a)$ groter dan of gelijk aan $0$.\n\nHet bereik van de functie $k(a) = \\sqrt{a+2}$ is dus $k(a) \\ge 0$. Dit geldt voor elke wortelfunctie waarbij de wortel niet wordt vermenigvuldigd met een negatief getal of waarbij er geen negatieve constante buiten de wortel staat die de uitkomst onder nul trekt.",["D",1785021319349],["D",1785021319678],"a618bd5f-a57a-4ae0-82ee-9cc412ae7034","hoe-werk-je-met-wortelfuncties","Hoe werk je met wortelfuncties?","werk wortelfuncties","Om met wortelfuncties te werken, moet je rekening houden met verschillende aspecten, zoals het bepalen van het domein, het vinden van randpunten en het oplossen van ongelijkheden.\n\n**1. Het domein van een wortelfunctie bepalen:**\nDe uitdrukking onder een wortel mag nooit negatief zijn in de reële getallen. Om het domein te bepalen, stel je de uitdrukking onder de wortel groter dan of gelijk aan nul.\n* **Voorbeeld:** Voor de functie $f(x) = 3 - \\sqrt{2x+5}$ stel je $2x+5 \\ge 0$.\n $2x \\ge -5$\n $x \\ge -2.5$\n Het domein van deze functie is dus $x \\ge -2.5$.\n\n**2. Het randpunt van een wortelfunctie vinden:**\nHet randpunt is het beginpunt van de grafiek van een wortelfunctie. Voor een algemene wortelfunctie van de vorm $f(x) = a\\sqrt{x-p} + q$:\n* De x-coördinaat van het randpunt vind je door de uitdrukking onder de wortel gelijk te stellen aan nul ($x-p = 0 \\implies x = p$).\n* De y-coördinaat van het randpunt is de losse term die buiten de wortel staat ($q$).\n* **Voorbeeld:** Voor de functie $k(x) = -2\\sqrt{x} + 3$:\n * De uitdrukking onder de wortel is $x$. Als $x=0$, dan is de x-coördinaat 0.\n * De losse term buiten de wortel is $+3$. Dit is de y-coördinaat.\n Het randpunt is dus $(0, 3)$. De $-2$ voor de wortel beïnvloedt de vorm van de grafiek (spiegeling en strekking), maar niet de locatie van het randpunt.\n\n**3. Ongelijkheden met wortelfuncties oplossen:**\nBij het oplossen van ongelijkheden met wortelfuncties volg je de volgende stappen:\n* **Stap 1: Bepaal het domein van de functie.** Zorg ervoor dat de uitdrukking onder de wortel altijd $\\ge 0$ is.\n* **Stap 2: Los de ongelijkheid op.**\n * Isoleer de wortelterm.\n * Kwadrateren beide kanten om de wortel weg te halen.\n * Los de resulterende ongelijkheid op. **Let op:** Als je vermenigvuldigt of deelt door een negatief getal, draait het ongelijkheidsteken om.\n* **Stap 3: Combineer het domein met de oplossing van de ongelijkheid.** De uiteindelijke oplossing moet voldoen aan beide voorwaarden.\n* **Voorbeeld:** Los $3 - \\sqrt{2x+5} > -2$ op.\n * **Domein:** $2x+5 \\ge 0 \\implies x \\ge -2.5$.\n * **Oplossen ongelijkheid:**\n $3 - \\sqrt{2x+5} > -2$\n $-\\sqrt{2x+5} > -5$ (trek 3 af)\n $\\sqrt{2x+5} < 5$ (vermenigvuldig met -1, teken draait om)\n $2x+5 < 25$ (kwadrateer beide kanten)\n $2x < 20$ (trek 5 af)\n $x < 10$ (deel door 2)\n * **Combineren:** De oplossing is $-2.5 \\le x < 10$.\n\nDit zijn de basisprincipes voor het werken met wortelfuncties.",["D",1769213749518],["D",1769213750321],"4476c83b-2ace-40e6-9a16-c2dad162055f","wat-zijn-de-eigenschappen-van-wortelformules","Wat zijn de eigenschappen van wortelformules?","eigenschappen wortelformules","Wat zijn de belangrijkste eigenschappen en beperkingen van wortelformules, vooral met betrekking tot de waarden die onder het wortelteken mogen staan?","De belangrijkste eigenschap van wortelformules, zoals $Y = \\sqrt{X}$, is dat de uitdrukking onder het wortelteken niet negatief mag zijn als je met reële getallen werkt. Dit betekent dat de waarde onder de wortel altijd nul of positief moet zijn.\n\n**Waarom is dit zo?**\nEen wortel is de omgekeerde bewerking van kwadrateren. Als je een reëel getal kwadrateert (vermenigvuldigt met zichzelf), is de uitkomst altijd nul of positief. Bijvoorbeeld:\n* $3^2 = 9$\n* $(-3)^2 = 9$\n* $0^2 = 0$\n\nOmdat er geen reëel getal bestaat dat, wanneer gekwadrateerd, een negatief getal oplevert, kan de wortel van een negatief getal niet bestaan binnen de verzameling van reële getallen.\n\n**Voorbeeld:**\nNeem de wortelformule $Y = \\sqrt{X-5}$.\nOm te bepalen welke waarden $X$ kan aannemen zodat $Y$ een reëel getal is, moet de uitdrukking onder de wortel ($X-5$) groter dan of gelijk zijn aan nul:\n$X-5 \\ge 0$\n$X \\ge 5$\n\nDit betekent dat $X$ elke waarde van 5 of hoger mag zijn.\n* Als $X = 14$, dan is $Y = \\sqrt{14-5} = \\sqrt{9} = 3$. Dit is een reëel getal.\n* Als $X = 4$, dan is $Y = \\sqrt{4-5} = \\sqrt{-1}$. Dit is geen reëel getal, omdat -1 negatief is.\n\nDeze beperking is een fundamentele eigenschap van wortelformules bij het werken met reële 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De grafiek van een wortelfunctie.pptx",5844621,"4HV De grafiek van een wortelfunctie",["D",1729097850300],["D",1729097851284],["D",1773044559782],{"_996":339,"_156":1020},{"_996":339,"_156":1019},{"_996":339,"_156":737},{"_996":339,"_156":747},{"_996":339,"_156":1018},{"_996":339,"_156":1017},{"_996":339,"_156":1016},"wortelfunctie tekenen","wortelfunctie randpunt","wortelfunctie domein","grafiek wortelfunctie tekenen","grafiek 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34,1053616,1053956,"j","5850e03b-9370-46c2-833f-8d09b5dfa848",3233,1053236,1053516,"4555e016-cd4c-4a76-a98a-ce0c4ec65c8c",3232,1053036,1053176,"45e0a881-e914-45ae-a80d-2e5266c70a18",3231,1051706,1052396,"-zeven","08e2ef69-e144-4bdc-8c80-73d808c35b70",3230,1051596,1051696,"02fef3d6-776f-4006-b730-f7df9632570d",3229,1051176,1051576,"8c4626dd-4036-4e87-9c17-b549979b7608",3228,1050996,1051156,"1f53c0a4-c00b-4194-8cdc-ac65b64de871",3227,1050766,1050936,"7153150a-35a4-442f-9bc4-1bb1fa2fbdf7",3226,1050596,1050756,"als","4ad54a02-42d9-4279-a4eb-c0e9c0a19a64",3225,1050416,1050556,"24cee5c3-decc-4b23-b2b0-495096cd9044",3224,1048956,1050376,"is.","250bf0fc-5284-407d-a6ea-e204f5f910f1",3223,1048536,1048896,"ed8a8226-0b29-49e0-8cdf-6485a65e517f",3222,1048316,1048456,"4a33e170-0968-4a64-ba77-14731719a353",3221,1047896,1048256,"46b3caa5-31c5-4311-aec1-cf01512f8d2b",3220,1047536,1047675,"a5ec7ecb-0930-403d-b906-a1d44df6bdcd",3219,1046626,1047496,"6887bea3-8ee9-4f1e-86ff-3d27f31b7b4c",3218,1046516,1046616,"4a111eea-d1dc-401b-af6b-6ead952aaeef",3217,1046436,1046456,"c7b82591-d212-4d42-a9e0-dd9c77c82d1c",3216,1046096,1046215,"70492726-f716-404f-9326-95068cc64b68",3215,1045656,1045956,"punt","4bdcc25f-9ba5-43c3-94ba-b1058d6bf165",3214,1045436,1045545,"c43f58ef-2de4-45b9-bfe3-624682daa9a6",3213,1045336,1045396,"op","023f2541-213d-4239-abfd-bfe5c6a48d63",3212,1045136,1045296,"7fd257bc-5847-4fc4-9d94-e736d453d1b4",3211,1044876,1045096,"8176f512-6f84-497f-bf7c-641970daa894",3210,1044736,1044836,"523742b8-da04-4e4c-a4ff-f77e22de9ba7",3209,1044496,1044715,"zitten","6fbd72f6-6a62-48f8-9a9d-7d9520a189c1",3208,1044356,1044456,"4d980b09-bc1f-41b3-ab32-46332ae37741",3207,1043496,1044296,"kijken,","5400ce9a-6b70-4962-adb0-e0ec53c71fc0",3206,1043096,1043436,"f481740c-015a-4fb0-b778-1269c7a91e65",3205,1042996,1043056,"7e7a79aa-a65d-4ae0-bdcc-3cd7a6a36af3",3204,1042876,1042976,"af02faa5-4609-4fbe-88b3-dd45a19e1e30",3203,1042516,1042836,"schetsje","7fcdc2ea-cc9f-4ab2-83af-6a2849059cd1",3202,1042136,1042456,"ad8f70cb-9588-49e2-8459-3b5393d182a1",3201,1041976,1042096,"68f97a6f-7659-4d7d-b895-918c629e4a72",3200,1041736,1041936,"even","5410498b-5278-4560-b474-d02c19b20117",3199,1041576,1041695,"dcdca4e2-3dac-4760-894b-42a85fff51ae",3198,1041496,1041556,"d9feb42e-0cf7-4f71-88f9-868f5a3a9e0b",3197,1041396,1041476,"Als","871d8cd0-9b4e-4490-9f18-7433c2cea8a6",3196,1039646,1040456,"-zeven.","c9f1bb74-425d-4fdb-8b4a-d5cd5785e12e",3195,1039456,1039636,"afb4b131-e54c-45c0-b7fb-8bbd1fbdae0b",3194,1039336,1039436,"7984f550-4247-4be8-876e-340c1657edd7",3193,1039195,1039316,"0b96a28c-e808-4f72-8b70-00afa499f8a3",3192,1039175,1039186,"2be30c08-e625-4c42-bee6-8da4d1e67db0",3191,1038836,1039056,"vullen","d14939e8-5044-4bd0-9eee-4aebe3c5e173",3190,1038736,1038816,"te","9186bfb1-6739-4240-94dd-5354e03c4048",3189,1038636,1038675,"e69230bb-0815-4580-a516-c28b510fa4c3",3188,1038576,1038586,"F","983d3486-349c-4b10-8d84-f9e20d1e33ea",3187,1038296,1038415,"5ac7147e-f858-432c-847c-7ebaeb61da74",3186,1037996,1038256,"functie","5d74d7f1-a656-4833-a98a-74bcc4a64426",3185,1037896,1037936,"9fb8b87a-fdde-4a54-a7f6-9d3df9b4a512",3184,1037816,1037856,"ac4165d6-289a-4f7a-b921-2bf2bfeebfe8",3183,1037616,1037776,"91c5f482-f96d-46e0-81db-68fae1e80831",3182,1037576,1037586,"4c804d3a-3a5a-492c-bdec-8c34678b324b",3181,1037556,1037566,"0be703dc-a3a5-4947-b4ec-9e58774fc549",3180,1037036,1037465,"-7","74756d55-30b4-4d4e-9ca4-66b1c962f8b0",3179,1036915,1036976,"baccb43e-7156-4c65-a24f-bee1e392fbcc",3178,1036736,1036896,"door","1ed7243b-ac04-45d6-b593-8171c14efb7b",3177,1035896,1036175,"06e6e33e-205b-4f20-9d4c-2b47deda73be",3176,1035816,1035866,"24a4716e-dc03-4ae7-aa37-1a93bcb81859",3175,1035786,1035795,"d724456e-c4dd-40b1-9a2d-5197c7bdeb7b",3174,1035286,1035776,"641c8115-8cee-4643-8b05-76fa6a49b297",3173,1034856,1035276,"precies","eb148a0a-8d0a-4857-9663-ea1877f4c445",3172,1034675,1034756,"152d274a-d4fd-406c-99ad-c64e744d821f",3171,1034236,1034646,"8998233d-0006-4994-98ab-d4483d78876a",3170,1034136,1034175,"b5c5d848-7d3c-47ce-bef9-d310ba5159ae",3169,1033996,1034056,"c7183523-0835-4447-b3ab-425b14a9c55d",3168,1033896,1033956,"41e10949-bfdb-4f50-b918-a32a093c7501",3167,1033796,1033876,"fd25e94c-4582-45a7-b89e-7c7b3b432a2d",3166,1033596,1033756,"e0257c52-b909-4901-9843-c56f50cf7c77",3165,1033276,1033536,"c39837dd-1ea5-405d-b837-b80d3f090f73",3164,1033016,1033236,"eerst","8367640e-1c54-468b-ba3b-11531aad6d3a",3163,1032936,1032976,"80fc2d1f-ec8d-43a3-ad29-dbee297654ea",3162,1032816,1032915,"Ga","453f4d11-2939-4250-8c54-07cdc93b5406",3161,1030736,1032796,"-7,5?","289b4774-4eb0-4813-a46d-9b33a9978402",3160,1030656,1030715,"72b58e7d-ddf9-4210-a17d-fb2ad42e7f42",3159,1030336,1030636,"533f630e-5f28-4c07-9cdc-86c23f0b9f7a",3158,1030195,1030296,"f4c34583-5ad5-4824-bd21-6fbfbe1f13f2",3157,1029736,1030175,"2a381899-7663-46fb-bbbd-891534f36e72",3156,1029536,1029715,"208aa944-c917-4a22-b62a-d2d15fb66cb0",3155,1029476,1029516,"59ae45d3-9350-4cf3-8c65-e9fbb4bfd17f",3154,1028996,1029175,"927f53c0-b13c-4b62-9884-0ffcae66c2ec",3153,1027356,1028876,"coördinaten","457ca683-cb44-457e-9640-286a869d6fe1",3152,1027215,1027336,"7e123b34-3452-4c66-89f2-80cb031577ad",3151,1027036,1027136,"d97300c1-9923-49c1-b0cf-d1bca1a65e4f",3150,1026876,1027016,"6222e138-2add-46f1-acbe-4be932de6aff",3149,1026736,1026846,"0c9ee80d-511d-4d89-90ec-ef5097df2a70",3148,1026436,1026715,"Oftewel","1052500e-699f-44b4-aeb4-b73658e5ee7d",3147,1026296,1026406,"aan?","60503954-4212-479a-a236-c763d73f92d5",3146,1026136,1026215,"a7330865-907c-42a7-9b4b-264d868c0c61",3145,1025736,1025996,"neemt","a9f7d746-cf51-4602-b72b-df306cc5473e",3144,1025516,1025715,"waarde","04a7db2f-5adc-471f-93bc-df4aa0063a5e",3143,1025256,1025496,"welke","eafe7889-e05e-4a0d-95dc-ed8e20d5d8fb",3142,1024915,1025215,"weten","01664677-0a71-4add-9608-25083bd33a3b",3141,1024876,1024886,"e0488fd0-577d-4e59-8a8a-491ad6e903f0",3140,1024695,1024866,"willen","de1bd6a8-1e72-440a-a8ae-07d5e81335c5",3139,1024596,1024675,"Nu","086c0e74-703d-4df7-96c3-4b963c120639",3138,1023936,1024536,"andersom.","6c3b99a1-9a7c-4bab-82af-a3ae74370eb4",3137,1023776,1023876,"c2f90720-6c3a-470b-8f2d-cc6f88fb02a4",3136,1023696,1023756,"f9374670-0d2f-4e12-91b8-8cb11e73eda4",3135,1023536,1023636,"één","60813cc4-1dec-4dce-86e3-d0386f3d6dea",3134,1023336,1023436,"0f2fada3-f371-49d7-a2a6-bf5adb94524c",3133,1023036,1023276,"f934034a-a50f-449c-a457-080f27daa00e",3132,1022736,1022836,"62c80c1b-f507-4af8-abf2-742c577c9b3f",3131,1022256,1022496,"72b9e1f4-4e1b-4875-a0e2-5c6d80e19825",3130,1021896,1022196,"4a199132-2c10-4aff-9c3a-6041a34fcd10",3129,1021456,1021776,"91c5ad16-2d9b-4617-bcaa-02905e27a667",3128,1020956,1021415,"gevraagd","38a16c2c-63a7-4131-baaf-0f8a1498137f",3127,1020796,1020936,"werd","4efbe201-f121-4bc5-a41d-33f0917f4002",3126,1020596,1020776,"net","c3d6fce6-e409-4585-8f80-97f93eb221df",3125,1020376,1020536,"74afe20a-c848-4dda-9142-080a20ce3ea0",3124,1018796,1020356,"-7,5.","e581054f-f94b-4231-9292-a9effa0d24dc",3123,1018696,1018766,"1bf44758-c67d-4641-af0b-74a4c18a0a49",3122,1018396,1018676,"27ff4ec2-3516-4cdc-aa6b-f8cdda24ae19",3121,1018256,1018356,"0ab68283-cdf5-45a1-abfd-b9d83bb849db",3120,1017936,1018236,"460f6b64-927c-48e3-9c26-3c4006ff6e49",3119,1017816,1017896,"dca53c21-abd3-4156-8ed5-9d6336ce38a6",3118,1017596,1017716,"191bc369-0513-45d0-9432-d1ad936f4ec5",3117,1017276,1017396,"92ce6564-3683-4c2b-a87e-08013b8f31b1",3116,1016956,1017236,"b387d7f2-bb99-4e38-84ae-017028e1bd15",3115,1016776,1016856,"40145c20-cafd-4826-99e9-af5a7aa44bb1",3114,1016336,1016596,"85be817d-f85a-4502-be41-00ff63a3d79b",3113,1015856,1016156,"c60c5933-6c99-4c24-b2cd-e2c23103dad3",3112,1015536,1015816,"Welke","a12f672d-c5fd-4db0-9894-642ba6aa5ebe",3111,1014756,1015496,"functie.","37436731-4ea5-43ed-a9f5-054c7e5c0814",3110,1014336,1014716,"dezelfde","3414cefc-bf81-4286-95d7-56c50506d749",3109,1014036,1014296,"steeds","add7b8d8-f8f8-4e87-89b2-493066447bc1",3108,1013876,1014016,"nog","3edcc9d0-fb7f-4086-86ca-f50fd95db8f4",3107,1013536,1013616,"06e23b31-0d11-449f-8acb-5d2cddb27414",3106,1012976,1013296,"beab2964-017a-4933-ac64-b5804d84d03b",3105,1012856,1012936,"69668155-d9cc-4018-8726-22c17a585ba6",3104,1012736,1012816,"2b44558d-72d9-4ff8-abde-b0084d95a61a",3103,1012296,1012716,"Gegeven","71b06d40-d8a6-4b7e-a1e8-f0a0011a3807",3102,1009656,1010196,"twee.","207dc923-d3e3-4513-8380-4a1334088546",3101,1009536,1009616,"d3e4e802-6bd2-4a47-b3bc-7eccd3659194",3100,1009376,1009496,"97a30667-0676-4268-bb92-4d59f5970e25",3099,1009176,1009316,"007c9728-1b8d-4f19-9efe-2ae9ea5a9137",3098,1008415,1008786,"snijden","ae799f48-96ad-430f-a11c-025b71f3d51e",3097,1008116,1008356,"elkaar","7ae92ff6-27db-4e42-9f8b-a47aae3ed45e",3096,1008016,1008056,"ze","c2d970f3-9323-4bac-8239-5b532547ed21",3095,1007836,1007976,"waar","bdc4ad03-70a1-4f06-9ef6-9031e4b2127e",3094,1007116,1007636,"snijpunt","e82cb87f-4e4e-40c9-89f4-b147d092ef2b",3093,1006976,1007076,"6b451797-2956-4ed3-9446-c19c8b565aa6",3092,1006336,1006696,"b8244984-f236-41e7-ad38-5555b2e261d9",3091,1006216,1006296,"17ae0a1e-1f6b-47bb-ac57-29616b5cc32e",3090,1006076,1006176,"b022daf4-7c7a-4701-8c15-85260b1b2298",3089,1005456,1005996,"21d34759-112c-4028-b506-801f6c74e5b9",3088,1005196,1005376,"8c35a929-2135-4dc4-9495-2b3f834ef602",3087,1005056,1005156,"ef4ca68c-aa4a-4d60-b4c1-c8d42cb5e093",3086,1004915,1005016,"21ce7572-42e7-4929-ac1b-cde1f1f3a8ce",3085,1004476,1004856,"2b6a3fa7-dc28-4f9b-bec9-0c98a07c45ab",3084,1004356,1004436,"83d7d18a-3c1e-4e3b-82a9-8b81a0326b2d",3083,1004016,1004296,"1b4120ed-6e4e-4df1-947d-f8a4d2ec4baf",3082,1003915,1003976,"4a843688-9de6-492c-b832-b5bbc4e052e2",3081,1003516,1003896,"bestaat","34c6f94a-99fa-4b0f-95e0-7287118dd6dd",3080,1003236,1003496,"6857019e-0e23-4ef3-b769-e9905f6e5e84",3079,1003096,1003226,"9757949d-7583-4ceb-be59-78f7578f80b7",3078,1002656,1003076,"anderhalf,","d6105d33-b13f-4824-9be4-b564ee16f0a4",3077,1002516,1002596,"ddbe1870-8b73-40ae-bb46-cf4269be4f47",3076,1002216,1002456,"7491da95-09cf-41e7-9e06-def3e0903104",3075,1001876,1002176,"f6825e87-fc49-4d13-9508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d-4e4d-864a-fe771ad3c3ce",2065,668339,668480,"min,","437905c4-c415-420d-ab5b-9d2471f2129c",2064,668280,668319,"777ad0a2-a6bc-4fd5-8fe0-8bafad4a000e",2063,667940,668140,"3aaca2fa-7f63-4957-ab91-0d38761644ef",2062,667780,667900,"7a8a434f-9a9a-4e3e-b13e-db7a8ead6de4",2061,667520,667740,"7e40e6b1-3f71-42fa-b15d-3afe0595a4f8",2060,667400,667480,"3b12ed72-0a67-434a-b3cd-10e847b124a9",2059,667300,667380,"e20dbcf4-4ce9-4c1b-882f-865ec3941c89",2058,666920,667280,"GX","c8f1278f-5074-4532-8617-8736bc34051e",2057,666579,666859,"90fca156-4a00-409b-8c74-2039b301220f",2056,666470,666520,"5eec59aa-51c4-4bbd-8550-d9cda4e14cb3",2055,666359,666420,"fe6dc49d-b719-4899-b3b9-effa0771ddc4",2054,665660,666319,"begeven","f547b8e8-6c25-4c5d-86fc-932c09947d06",2053,665500,665560,"561319df-5805-46f7-b615-05fb98afaa84",2052,665099,665410,"e7ddfeab-e0b4-4258-b359-deda0290d704",2051,661859,663660,"40d57121-4246-4e77-95fc-c25a1cb22b7f",2050,661380,661839,"bb20b87e-8a2b-47e6-9cee-ea9a5e14c427",2049,660980,661260,"07182152-9962-46c2-92f9-faa144c13ae5",2048,660460,660680,"691bd503-a3f6-4b67-a88d-b9d9bbb61a9d",2047,660119,660439,"7ed66f10-60ec-4238-ae1e-6d8c735db27b",2046,659819,660060,"db65b920-a90c-41bf-bb94-a22ec1220601",2045,659640,659800,"37a20b05-9da8-4bae-a510-3824d70b0bdd",2044,659500,659599,"4086f583-bd39-49f9-8861-06f14c2cc055",2043,659359,659480,"b935598d-37f2-4bbf-8c46-5eb39dd5c320",2042,658859,659339,"7147edf1-6dae-4a77-80ad-574bc1f75a2c",2041,658720,658819,"3ab30a57-871a-49f8-912a-ea1032da2b12",658599,658700,"7279af0c-b783-4f1c-9d20-8f98b1d49870",2039,657660,658579,"wortel.","88bd08e7-67ab-4f9e-a5da-3242ac380304",2038,657560,657640,"a6b32f3b-4fd0-4809-8067-371472e5bd4a",2037,657319,657520,"0e9557ad-6fd7-44b8-a204-d73556e0249c",2036,656900,657260,"f00bb969-1680-4f13-bde9-9ee7b9de8961",2035,656240,656800,"positieve","3caa2d93-ea7d-4836-a788-0907660cbd2e",2034,656020,656220,"24cf9576-2c82-42b6-83c4-619cc58ff985",2033,655880,656000,"f0c06bbb-950b-408e-8b7c-e60d0fe4bc15",2032,655859,655869,"387c281b-be57-49d8-8351-95c2fcdca3d2",2031,655640,655720,"9c23eabb-c246-4753-ad13-060e0fb218e0",2030,655300,655500,"777ed016-b28e-499b-8cc4-43ce9efb9920",2029,655140,655240,"89b671ce-eb6b-487d-8ad8-347ebff0eb29",2028,654800,654999,"c5d5ac0f-ae03-448b-a86c-7ce5edb16c18",2027,654359,654599,"66ace94b-c49e-441f-9ff1-57acc95d2402",2026,653980,654119,"0cd1d914-9423-4d04-b1ec-2fda53319b56",2025,653740,653960,"principe","c35db1ed-b00c-4146-8b6c-86fced622109",2024,653619,653680,"0c4169c2-ef2f-4548-8e05-f8ffaf9c4650",2023,653420,653599,"13a1c8ab-17dd-4468-8e5d-b74f0c7654d2",2022,653319,653380,"12ff21d1-4502-4e8d-9d79-bd3950048e13",2021,653240,653309,"ed896d00-4c8c-42f9-b8e2-bea9f7ce4dc3",2020,653040,653230,"92bb4f17-e7ee-47ee-9b08-72efba0e5916",2019,652700,653000,"37a37500-b1d8-4d2b-a9e6-9b15adc2f248",2018,652560,652660,"fc2d4c5a-97c9-42af-a51e-8ad76a4497d8",2017,651700,652119,"plusje","cf33ea84-4ae7-4a7b-934d-2803bc02ef2c",2016,651500,651680,"2a81a40f-0fc1-43fe-81c8-abcb4a6c441d",2015,651359,651480,"Bij","14ec499e-374f-4ec1-b465-38c5c1f53986",2014,650880,651349,"getekend.","d04564cb-3fd0-4cd6-8bea-be3b380617fb",2013,650750,650859,"heb","8424f1bb-5136-4b1e-abd0-df6bc1ea4415",2012,650500,650740,"lijntje","71383594-21e1-4fe8-b002-653f61115182",2011,649980,650200,"zo'n","a8b7f0a4-66c6-4bc4-85f5-4a7a58065940",2010,649540,649819,"geel","229dbd03-9328-47e6-9cf3-87576bf32d3f",2009,649359,649500,"51ec0503-27ec-4b9e-bee7-eaa921326de1",2008,649280,649339,"d4021dbd-19c2-47c2-8d7a-f388ffc058ff",2007,648920,649200,"9f457252-c7f7-4fed-bc1f-04652e0f12b1",2006,648819,648900,"9600acd2-83f2-4abe-ac91-4527bc9245c4",2005,648740,648780,"f1275e5d-f7ed-43f2-9983-eef4c0d1bf33",2004,648520,648730,"Vandaar","007a5066-0ae4-4c84-91e2-c6593d7fc7b4",2003,647619,648440,"16965127-2146-4ef4-ab29-22aac9d4f359",2002,647480,647579,"6be9d25f-8ef9-4911-a658-0cebdd94342a",2001,647240,647460,"b42e95f3-3145-40de-925b-6c7fd4240dc0",2000,647079,647170,"54d50274-14bb-4df5-9909-30768d41b44b",1999,646800,647060,"09756937-fb18-4671-b96e-fbb7d0161329",1998,646420,646780,"8132d7c6-76ee-4c32-94f0-9156651514b9",1997,646119,646400,"f56832b3-a36d-4160-9bac-3938d55a6efc",1996,645760,646079,"9cd5495d-4727-4d48-8eaa-b4227db6f130",1995,645599,645730,"20c122fc-f045-4977-b9b6-3532d1d98c4f",1994,645460,645579,"dbee35b2-ceb0-40fe-ab86-886ebdee8f71",1993,645400,645450,"2826d525-eee6-472e-8660-77e3e50bcc12",1992,645280,645369,"4faa0a22-f9bc-4449-8e32-b7edd31f1ce2",1991,644339,645260,"oneindig.","b216e318-b10a-4837-b4da-4daedf000c8a",1990,644140,644300,"8d680dba-be9a-4682-afbb-56e481305540",1989,643980,644060,"df4d23e7-388c-4f0b-96f2-83324997e652",1988,643800,643960,"02b9526f-e0a3-4614-8fd9-77ded03f1608",1987,643640,643760,"71f1a493-e75a-44b2-873e-2c632867e10b",1986,643500,643599,"fc48f75f-bcb2-45dd-9e1e-86c73670e598",1985,643359,643460,"be424e6e-d3d9-4fd8-879b-c0dfd2e51ec7",1984,642520,643260,"5200a88e-c2f2-457a-811a-fe2c76dc2b24",1983,642300,642460,"e937b382-c2a5-487c-80cf-4fdccba64e6d",1982,642140,642260,"da0e342e-c5b0-4e6b-9e5f-4a61673f1fb2",1981,641940,642099,"6de94de1-ab11-4999-82d0-d7179e3a726d",1980,641720,641880,"b6e4417f-1a50-4036-b327-745703ff139e",1979,641560,641680,"50eb5905-0f22-465a-8759-4b169652ff4d",1978,641180,641520,"930f7d48-6c28-4d3f-acf9-fe88279ba132",1977,641079,641160,"d0d2319c-5aa6-4c2f-8533-edda5d746db9",1976,640900,641040,"06fa0cfd-6e04-419b-9df9-fb5257863deb",1975,640750,640849,"1a33cbe9-30f7-4039-bdd3-ad4918c661e6",1974,640180,640740,"kijken.","323d416d-ea1d-45df-98a9-f2ce7f8bbda0",1973,639960,640160,"39e86a6f-8189-4ea3-b38c-61b6f6af1e8a",1972,639859,639940,"8c06efae-0b37-4d94-912f-f4cca3378dc3",1971,639800,639839,"40cf3add-8010-4e97-b275-5bedee61b024",1970,639680,639770,"608f2a7e-d1be-4319-865f-90cb329f3b1c",1969,639579,639660,"b869aa9a-2ae2-413d-b8f4-1e3edd335626",1968,639460,639560,"439a4152-5484-49db-ad04-c86ba37420d6",1967,639160,639440,"iets.","a676e7cb-fc99-4432-ad86-05d95126058e",1966,638980,639099,"b2025263-cf9e-40f6-88c9-b385a8e6d4e6",1965,638839,638920,"29e83a2d-6b71-4225-8703-d7cc09936909",1964,638560,638800,"10d40512-42cb-4a39-b2e0-332bfc3e8111",1963,638319,638440,"5d0c60e5-b1eb-47d3-b225-7a2e017b7d84",1962,637980,638280,"zes,","08a5c410-4af2-4e36-ad07-13c62118cc7a",1961,637740,637900,"d262dfb6-c84b-4e86-a1df-25558c253269",637540,637700,"5dac22e9-26fd-44b5-a9d8-9b6a949db17a",1959,637160,637520,"c9dda561-9ccc-4ea2-b3f5-2c76023550dc",1958,637079,637140,"88d95486-cdff-4f4d-a0f5-ff13bccce36b",1957,636819,636880,"7d005992-f9db-46f7-aa68-959bd4d25097",1956,636040,636800,"randpunt,","a7d58209-5905-41ab-a5bc-8ead02090b4a",1955,635579,635859,"97377fae-fd1e-4d86-9c6d-a2de700f792b",1954,635380,635520,"Nou,","85fda210-cc81-40f2-a870-7b0b1e03c59f",1953,634839,635359,"d97f9781-8655-4ffb-95dc-340bf000d106",1952,634740,634819,"2d5cbc9c-355f-411b-abe9-e03d27a8e950",1951,634579,634720,"941b4b0c-635b-4851-a241-c36f8ad31fcb",1950,634300,634420,"47a3445c-7560-49a7-9efd-0887f6e8539d",1949,634099,634260,"352fc2df-151f-42ed-9984-b43a6ad3f261",1948,633640,634079,"0e76675b-e378-4c5d-a918-2deb1f3c9e42",1947,633520,633619,"fd06d3fc-0d56-4d47-939a-27b280827502",1946,633240,633500,"Oké,","0b82d9bc-ab98-45a9-bb36-6789ba8ef011",1945,632060,632319,"2870e574-2685-4a32-b7dc-ab39d6389b7f",1944,631700,631940,"35955654-eda1-437a-ba1d-48370b038cb9",1943,631520,631660,"502a7b5d-2187-4caf-b5e1-be5342bd112e",1942,631359,631480,"51978d2f-f5a4-4a11-9196-b9e142de4dc6",1941,631160,631339,"3724572e-22c3-4297-ac0f-6e112f4880aa",1940,631000,631099,"d0f08e78-3af0-4e4c-a84d-9dbac24c475b",1939,630680,630990,"invul,","971cd0f5-28f1-4526-a2d9-abddfdec1c32",1938,630480,630619,"e9fa6783-272c-4b12-a123-ed6a658e5e81",1937,630339,630420,"2d0829fa-0a3a-4173-b4e8-d7f96a3b04ad",1936,629980,630140,"619407b7-58bf-438f-b11f-8b367887ecc7",1935,629700,629920,"04cba237-25cb-493e-969e-fe25f79cbffe",1934,629579,629640,"9a3e4cbc-505d-4d9d-900b-3e1f27981aea",1933,629280,629540,"6fc9012f-2bf6-48d7-b431-352462459d0e",1932,629099,629260,"72453a9e-1821-4c87-a7fb-7eded5629cfc",1931,628859,628980,"114d5462-260f-4e23-a058-526211baa177",1930,628480,628819,"f284a042-3475-4792-90a5-f5678ca3ed7f",1929,628380,628440,"06483387-a345-4827-bda7-74cfa6994e6c",1928,628300,628349,"9d664b08-0dfa-4619-8fca-a3b7b5d4ae83",1927,628220,628260,"ae0ba6b2-833c-4080-b672-35aac4869cb5",1926,628079,628180,"15686aec-10a2-498f-82fc-c4bb1745c0cd",1925,627020,628000,"invullen","d9912742-706c-4827-8431-a794e4bbc263",1924,626480,627000,"direct","b12e9d23-a613-4c29-83bc-e1794ac930e7",1923,626280,626440,"cbc816ac-d7f3-44d1-ae2e-077564df0d45",1922,625880,626060,"cc79c40a-0ceb-4aa4-8409-5302eeb36ce9",1921,625780,625869,"65529406-3916-44fe-9f95-88a9a95efb2a",1920,625540,625760,"9090f9ba-97a4-4984-bc33-c4913f0e0acd",1919,625280,625440,"42151704-55a1-4a95-95aa-16fca5542e73",1918,625020,625200,"f6a5fae1-649d-421c-9b5f-78ffcc299e28",1917,624819,624980,"7c02181f-8358-44e4-b56e-9c4763ba2186",1916,624579,624799,"5740e84d-05e0-444f-b92b-8b19f7199354",1915,623780,624540,"uitgerekend.","ed3e4d1d-becb-4272-bab8-8735f9cd09a5",1914,623099,623700,"ongelijkheid","cacf50c5-b43d-4e8c-858e-930f08343b3b",1913,622960,623040,"d3f7e28b-ea30-4bd0-959f-d57904322079",1912,622839,622940,"35cde043-2c5d-4742-87e7-ba7260785415",1911,622599,622819,"6733238c-e523-480a-9251-6d84bf9a60d9",1910,622460,622560,"0cef51d7-9a7c-4601-9531-b7bca0c87141",1909,622319,622440,"5baf3182-2617-4cef-8188-17716ab72548",1908,622180,622280,"859ab2a8-e48d-4b6c-81b7-ac3920f73807",1907,622060,622160,"f8c09f39-3d9d-44b9-bf20-d2f328fa4d07",1906,621858,622049,"komt,","a96915ff-cd8e-498f-ad11-c40ee7f6feb4",1905,621700,621839,"uit","1b51e4fc-f183-4213-9e3f-12ef5a44c4eb",1904,621460,621599,"48b6d9e6-7872-46f1-9913-6082a029f25e",1903,621239,621419,"bb640f58-516b-46bd-bdc0-96fdd23ba3d2",1902,621030,621169,"0d4ce8d9-1b91-4d29-903a-29e30d75c618",1901,620900,621020,"2d75fe16-5e93-4ca6-aeb7-d870ccde300d",620619,620760,"548e9d75-d654-466b-96a2-d50f1392afa0",1899,620319,620540,"9a8c38d4-b32a-4be8-874d-60656df3d1b4",1898,620160,620280,"0f01ae58-2085-4b6b-8649-0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199760,200040,"ec91fbab-55eb-491f-b42e-d171448b41b3",621,199540,199740,"7d5bb9d1-bbf9-4829-91ac-ede17bb37ed0",620,198980,199329,"b6d7c9cd-ef7d-4fb8-a3c6-560a6d2a592b",619,198140,198920,"gekeken","9f75d0ab-c3f1-4813-86ae-4d8ca5e9f46c",618,197960,198120,"7c57db25-ed9b-4f60-8269-27e12065f841",617,197760,197920,"hebt","a5d2617c-2e26-4a62-b0fa-5bdcd87faacf",616,197660,197720,"a8a9964e-8d9b-4420-aa9f-c4411ca24d75",615,197520,197640,"2bdbb5a9-bff9-4d63-96b0-d43815cb134d",614,197040,197480,"logisch,","00a58701-fb4f-409d-9f64-7e716b6f4cae",613,196680,196940,"be2cd5c3-1930-4b7b-8647-2f27a72f7e7d",612,196590,196640,"a0b80c97-2909-474c-8519-96db81b3f254",611,196500,"df13c7f3-64b9-4a6c-a2e0-d4619aa62647",610,196440,196480,"d4949c39-04b7-47b0-9312-20cf425d54b3",609,196200,196420,"f893b78d-a07d-47a5-8419-89d2769eecbc",608,196020,196160,"d1cec1db-0b67-429f-9ebb-bf0db54d722c",607,195720,195980,"b935e087-6ed5-4dd2-b1ec-939b4fb358ce",606,195620,195700,"449de2b5-9196-40db-a8e5-9d6c8bada96b",605,195520,195580,"02497f0b-2577-4526-8c64-1e7754cbd900",604,195000,195480,"13dc3600-34f4-4789-ad24-6555b5de26ea",603,194820,194900,"c9c73b27-7c8e-4ecb-ba21-5c27bcba03ee",602,194560,194740,"0b344a6a-5f39-453d-9514-ac5cc93da0d6",601,194420,194520,"edc8b3b4-089a-45be-9a6b-697d4e0e804e",600,193720,194320,"5012b722-5b5f-4a1a-b0fd-7e24650992e6",599,193560,193640,"9aabd368-9b43-4282-9f35-57b51d1da70d",598,193380,193520,"6b23cba5-fad4-417f-9bbb-80a62900795c",597,193180,193340,"fcd84b93-8df8-4332-baef-9497d49f5f95",596,192760,193020,"b1a72002-106c-4e81-9f7e-d4a4fcba78f3",595,192600,192720,"c0e6fdf0-3624-4c8f-b592-00e6e820a52e",594,192280,192540,"64d9539e-63ea-48b2-bdce-536f6bc560a0",593,192200,192260,"05a740be-cd0a-40ee-8fe5-875166280bf0",592,192100,192180,"03942b68-7dda-47bc-9036-b2aa4a98cffa",591,191880,192080,"aacf0201-b41a-42cb-8ccc-fa7e8b8a77a2",590,191760,191820,"28035491-91cc-4880-ae7e-132717ab01e3",589,191329,191740,"Maargoed,","0a4e116e-e72a-4e38-9faf-66bdcb503466",588,190520,191320,"92f1eb57-4d85-4a31-91de-b50f23fc415c",587,190000,190460,"59ba7d2b-59ec-46ea-9ef7-63d56cf4d40f",586,189680,189780,"a9c3812b-d836-4bc8-8008-b0a02715b32c",585,189580,189640,"e828ee3a-6408-4c56-ba9d-ac9c67dd33a9",584,189440,189560,"e34bdea8-aefc-4033-a2a8-1c94c3a8b257",583,189200,189400,"8818ff77-cb7a-460b-a2ad-36ea704250c3",582,188300,189180,"b8031cb3-0076-4583-935d-15fdbaf50b06",581,188160,188260,"d21558c8-9079-4d22-9600-1c7fbb3f4adf",580,188060,188140,"92116f1b-f04d-45ed-89ab-3e60170d0ced",579,187640,188040,"71beb7d1-56b5-46e0-b642-ed2eb72cfbf9",578,187260,187380,"8815a20f-0ded-4515-8af9-40fffb9542ab",577,187100,187230,"35786ae0-76e4-446a-b15f-e79836fc5da9",576,187020,187090,"ecfaa3b4-921e-464b-92d6-f5780a949261",575,186860,186980,"5c21b7b8-e46a-4e15-9450-2149d0f92855",574,186800,186840,"64f4513f-e05b-49df-8c3e-ae93704f0f66",573,185640,186760,"beginpunt.","ab60d7e5-b106-4e2d-9eba-219ca40e218b",572,185540,185600,"9b1ac668-1061-4624-aacd-2eb9d5960b3e",571,185080,185240,"47520b21-6dd4-40de-a087-bd352b5f54a4",570,184880,185020,"da67997a-0369-4e75-828f-da8e8d811b9a",569,184700,184850,"0da7e960-50c0-48ac-8af5-bf069607bb35",568,184120,184680,"e81dec76-fc8e-4f1d-9dc6-46b37edf99ea",567,183960,184080,"d3a18130-5cea-4399-9acc-b1e1258b1ff4",566,183600,183920,"d819dc84-4f5f-44b8-835a-877a627f8d80",565,183180,183520,"f9d49e81-f2b8-4047-a3f1-5a70d7056c7f",564,182989,183160,"39086e64-24b9-4373-a79d-8bb55e3caf0d",563,182800,182980,"919c853b-2c01-4441-bf20-efb0193720ad",562,182600,182760,"8673a28f-49f3-4c07-aee3-7ed803b0475a",561,181840,182560,"31cc1959-59a4-4247-8238-34461a4f0f1e",560,181720,181800,"f88a071b-a206-43f1-a7f5-e97d7bb6dfcd",559,181560,181680,"0d574cb6-00e9-412b-89ef-53f8e76b01d2",558,181400,181540,"4c88f99d-f585-45c1-88ec-a51e7d7669b2",557,181060,181240,"8cdd3bbb-d8c2-49f1-b12f-c327bbacf99a",556,180880,181020,"c59e3eee-6e7b-4170-96a5-ecf608c10853",555,180700,180820,"6d521c9d-1bfe-4081-ba41-f58e8f66c9dc",554,179900,180480,"cb29ead2-6e06-4dce-b4a9-3c6c60676848",553,179700,179840,"481a69da-5ad0-4892-a796-334da30a3871",552,178760,179660,"3ad70677-0345-4c59-8f48-dbbbcec3b17d",551,178580,178660,"7e164e45-e2e5-429d-8670-7e1852ca47c8",550,178480,178540,"95e02715-538b-42a3-80ab-2057923cfb4b",549,178340,178430,"96aa87ec-375b-4660-844a-bfe22a8c389b",548,177860,178310,"90444e10-1674-49cb-840f-2f757ee79f8d",547,177420,177820,"84e190d2-4be1-4eb2-a494-e561ea284774",546,177300,177380,"44423b32-842e-401e-8656-8a4dd9ba4fd0",545,177240,177280,"614be309-4495-447f-8664-f6b0ee30f306",544,177100,177220,"601aafe8-19fd-44ae-a22d-9511e5f1eff1",543,176960,177070,"43772f28-b83a-48b8-9981-3f769a8e101f",542,176800,176940,"5971c3b9-6903-4448-b145-512fa9c219f9",541,176580,176780,"529c9e6b-39aa-4540-9fd0-30e9354a8984",540,176260,176560,"f.","afae89af-ac93-466f-b451-975c25b206b6",539,175920,176160,"6edbb6ec-09c0-445f-863d-f465236b0bfc",538,175390,175860,"244c5b21-295f-48b0-96da-f3db289ae4d5",537,175220,175380,"d000c19c-934b-410a-ad80-e8c9e1b3f589",536,175100,175200,"e41cf4a8-c675-4483-a9ee-29019036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half.","e93904bf-0f4c-4e2d-ba58-436d7bf4e89f",1002640,"Want daarna bestaat de functie niet meer.","bd863a69-1e34-49e3-ae11-22ffc8994f5e",998640,"Dat kan, maar x moet wel kleinig of gelijk zijn aan anderhalf.","693a1220-f4f8-4c4d-928e-75b404fa55d8",994640,"Dus dat betekent dat die fx is groter dan 1.","16310c25-44fa-41f9-921d-499f12285df1",991640,"Dus het gaat maar tot en met die anderhalf.","bc2cec27-c962-4ae5-806b-e8707f437d65",988640,"Dus hij kan nooit verder dan die anderhalf lopen.","5ec5543e-69c2-4f10-9e6c-3bd7cd15ca87",984640,"En de x-coördinaat van het randpunt, wat we hebben ook gezien, is anderhalf.","9ffe7baf-65f0-445e-9b67-6dda7d9bcf89",980640,"We hebben net gezien dat het domein natuurlijk maar loopt tot aan het randpunt.","54d2181b-17af-4331-8ffd-b614189e3031",977640,"Maar pas op, niet alle waarden van x doen mee.","ae0bab72-da78-44b4-b434-3b1724650299",972640,"Dus dat betekent dat fx is groter dan 1 is als x is groter dan een half.","971a1108-cd2b-42f1-a46b-0651dbad1bd5",966640,970640,"En dat is als we vanaf die x is een half naar rechts toe gaan.","43e0d972-e518-4c3d-89a2-569379b25113",960640,965640,"Oftewel wanneer ligt die blauwe grafiek van f boven die rode lijn i is 1.","4059d50a-a2a5-4971-ae71-f0840b6f8b5d",957640,"Maar de vraag is wanneer is f groter dan 1.","f847621f-52c8-4df4-bbf4-767ad0463414",955640,"Dus dan zijn ze allebei 1.","5b752fd4-11f8-4ec8-b184-c3b2f1a47899",950640,953640,"Dus we snijden elkaar bij x is een half.","851fbcbc-5c4c-4597-8d74-cc71713d0570",948640,"En dan geeft dat x is een half.","eccca118-b11e-49af-9ead-c78d6b921fb0",942640,"Dat doen we door optie intersect of als je rekenmachine in de Nederlandse taal staat optie snijpunt te gebruiken.","2a364cd1-2171-4dc7-9f11-56aefc66a198",936640,"Om dan te kijken wanneer die f groter is dan 1, gaan we eerst kijken naar het snijpunt van die 2 lijnen.","883a5e68-c9d8-4ab1-84c2-a5fa1ac72711",927640,"Dan voeren we de formule van f bij i1 in en dan gaan we vervolgens bij i2 de lijn i is 1 plotten.","125e7014-6b9c-4fbb-8e01-c89e9b18265e",922640,"Als we moeten oplossen wanneer fx is groter dan 1, dan staat niet exact.","94bb7e96-15af-4bb9-bf65-f3bd69f97b87",919640,"Los op fx is groter dan 1.","696bbdb8-5e2e-4e44-9d2c-edb4f1e916f4",913640,"Gegeven is de functie fx is 5 min 2 keer de wortel van 6 min 4x, nog steeds dezelfde functie.","343b2710-a185-43a0-9057-cd6f8e8de874",911640,"Opdracht 2b.","454f9784-1a3d-4358-957e-e278304780cb",907640,910640,"We verbinden de punten en dan krijgen we deze grafiek.","7ea871f0-98cf-4911-8edf-4fbff410e850",904640,"Dan tekenen we die punten allemaal netjes in ons assenstelsel.","3073ed23-f427-4c5a-b300-c2c0213e96d2",900640,"Dan maken we een tabel bij de situatie.","acba97c6-c183-4433-9152-9527c562dc68",896640,"Dus die 5 is de hoogste waarde van het bereik en dan gaan we naar min oneindig toe.","75ef764c-d99f-46bd-bd04-6f1eca57457a",893640,"De factor die voor de wortel staat is min 2, dat is negatief.","3f10830f-5fb8-474c-a197-2858fc895ef1",891640,"Dan kijk ik naar het bereik.","7e6f9907-40ad-45de-af90-d1bf7a123444",886640,"Zodat ik weet wat ook de i-coördinaat van het randpunt is en dat is dan 5.","f2161de9-5db9-4336-9496-c558011a9b2f",883640,"Dan vul ik op de plek van x anderhalf in.","521d9f36-06d0-4e09-ae26-09284efdbe14",878640,"Dus het domein van f is min oneindig naar anderhalf.","e94c5301-99cf-48cc-aa26-cfd34e7dcdb7",873640,"Min 6 gedeeld door min 4 is anderhalf, dus x is kleiner of gelijk aan anderhalf.","01eedb95-eec2-4804-83c7-3baf705b6a47",868640,"Dan moet ik delen door min 4, min 4 is negatief dus het teken klapt om.","eeff9af0-f436-4bcb-b92b-05488d045b42",864640,"6 naar links halen, dan krijg ik min 4x is groter of gelijk aan min 6.","b89a79d0-278d-4143-8363-91c21be98f64",858640,"Dus wat staat er in de wortel 6 min 4x, dat moet groter of gelijk zijn aan 0.","d9006749-d595-4ed0-9827-ee1ef1203435",855640,"Dan gaan we eerst het domein bepalen.","c8671e47-e6f3-43c9-b8c7-c3887012a803",849640,854640,"Teken de grafiek van f en geef bf het bereik van f.","bd74b55b-1ed8-473f-998b-2c05cbaa8009",844640,"Gegeven is de functie fxx5, min 2 keer de wortel van 6 min 4x.","83abf759-4136-4bde-9c54-a16132f0ab49",842640,"Dus we zijn er bijna.","799aaf39-6de8-400a-8d53-27ba2d54a58e",839640,"Opdracht 2a, de laatste opdracht is 2.","66209267-a2bc-4fde-8bfc-8efbcec85f3e",831640,837640,"Dat betekent dat die 10 de hoogste waarde is van mijn bereik en dat ik daarna naar min oneindig ga.","60cad288-afb9-4f04-9774-3490c7a605c8",827640,"Daarvoor kijk ik naar de factor die voor de wortel staat, min 3 is negatief.","62345d68-4458-4056-8d5a-6b156fe96e9f",820640,"Dus de eicoördinaat van het randpunt is 10 en daarmee kan ik mijn bereik gaan bepalen.","98d96022-7253-4056-9a26-6b05071346f4",812640,"Als ik nu in de functie van k op de plek van x2 invul, hier komt dus 0 uit, dan krijg ik dus 10.","ae2120c3-fc79-4ff5-a261-6599f82721d5",807640,"Dus het domein, de laagste waarde is 2 en hij gaat naar plus oneindig toe.","bffd78bb-8d0c-4ed8-8863-c5f8aa91e7fa",805640,"X is groter of gelijk aan 2.","183d3ff0-d91b-4a99-9219-dcdd71ed084d",801640,"Vervolgens delen door 5, 5 is positief dus het teken klapt niet om.","23652642-17e8-4acb-9663-2c15917e2be7",798640,"Dus die 10 weg is plus 10.","f061c7ce-a9e6-4f16-b318-8744093c5135",796640,"Op deze manier bereken ik het domein.","bb43714f-9020-4665-bd28-f243d04d3f4e",792640,"Ik noteer wat er in de wortel staat en dat moet groter of gelijk zijn aan 0.","2285a0a3-2a64-4d09-926b-7426437715ea",790640,"Ik noteer die functie weer.","120bf31f-bc7d-4824-a926-b5c0e8561967",787640,"Nog een keer deze met weer een andere functie.","0b8b2840-544f-4ae3-865b-467c7b926aba",784640,"En dan de laatste voor opdracht 1.","4ff7e45f-7732-48a1-b4c7-9cdd57b309dc",775640,"Min 4 is negatief dus dat betekent dat het bereik nu die 7 de hoogste waarde is en dat hij naar min oneindig gaat.","7efd29c9-ed37-4085-8bd0-f82246ee15bb",771640,"Dan ga ik kijken naar de factor die voor de wortel staat, dat is min 4.","427d691f-8db7-4d51-988a-9c485e46e879",769640,"Wat betekent dit voor bereik?","10fb6694-8971-49c4-9a9d-44baefd7abf0",767640,"Dus 7.","4d2a68e0-bcad-440d-83ce-9dbb1476a368",763640,"Ik weet hier komt 0 uit, 0 keer min 4 is nog steeds 0, plus 7.","914dbb8b-91e4-4a73-bd2a-fbe0d3bf6515",761640,"Dan ga ik een half invullen.","271529d3-7bd6-4d8c-b6d5-12a89f25e476",758640,"Wat is dan de eicoördinaat van het randpunt?","f5df34bf-1fb8-43de-8715-199cb9682cc3",753640,"Die half is dus de grootste waarde en hij gaat daarna naar min oneindig toe.","a7b3aea4-e24d-4e16-9037-b69c7c6f1c1f",750640,"Wat betekent dit voor het domein van h?","a5fd7fec-d3f9-4781-accb-6115e9849be4",747640,"Min 5 gedeeld door min 10 is een half.","65f8e131-3ec9-44ff-8f6a-f3a8cce3709d",742640,"Vervolgens moet ik delen door min 10, min 10 is negatief dus het teken klapt om.","efb02472-3763-44ba-af25-3a9fc9eb0c38",738640,"Min 10x is groter of gelijk aan die 5 naar links, min 5.","ded63956-8137-4ccf-be8a-d46b45dea842",732640,"Ik neem weer over wat er in de wortel staat en ik zeg dat moet groter of gelijk zijn aan 0.","2263bed7-32c8-4f13-8aa5-48b220b96353",730640,"Dus ik neem h weer over.","c155968c-5276-4f1c-b12c-9672405839a1",726640,"Dit gaan we nog een keer doen voor functie h.","37ee9a3b-5331-4dd2-ba37-64cb9f9ae768",719640,"Dus dat betekent dat min 8 de laagste waarde is voor i en dat hij daarna naar plus oneindig gaat.","d51aef08-0062-4ff8-a307-170baeef7b2d",715640,"Daar staat weer niks, dus dat is positief 1.","70a3f37b-5bdf-4e28-9b46-0add1ca7cb51",712640,"Ga ik weer kijken welke factor staat er voor de wortel.","530e7307-62ef-4ce8-9423-745698ca2d9b",709640,"En wat betekent dat voor het bereik?","913a6e64-2674-48f6-9a82-60949ad33157",705640,"Hier komt dus 0 uit, dus de eicoördinaat is min 8.","4a3c7d3e-06c5-4508-adfd-76d0ed8f6f64",697640,"Dan ga ik de eicoördinaat van het randpunt berekenen door in de functie van g die 2 in te vullen.","a672a0cf-a596-4bdd-ac64-2602894f620b","Dan betekent dat voor het domein dat 2 dus de laagste waarde is en dat hij daarna naar plus oneindig gaat.","5f6e3d05-7971-4252-afc9-7aa43c2fae24",687640,"Dus ik krijg x is groter of gelijk aan 2.","0e1c669e-e570-4f47-a813-e5787dd9fb34",683640,"Nu moet ik delen door 5, 5 is positief, dus het teken klapt niet om.","79912569-e25b-4995-bbac-fc4130de6d1d",678640,"En dan ga ik x vrijmaken, dus plus 10, dan krijg ik 5x is groter of gelijk aan 10.","d42a3fe4-e464-44af-959c-d96c7361edc0",674640,"Noteer weer de functie, dan pak ik wat er in de wortel staat, neem ik over.","baaaccf6-37bc-4afe-9a0a-b25fb23f8bfc","Nou, dat gaan we dus nog een keer doen.","e249b82f-40a9-47c4-bc15-34cb68032252","Geef het domein het bereik en de coördinaten van het randpunt van de grafiek van g.","21ed8259-bb39-48e7-85ef-134f0016eb9d",662640,"Opdracht 1b, gegeven is de functie g, x is de wortel van 5x-10-8.","c5119bfa-126c-43f3-9893-0fc2ba0142de",661640,"Dus dat betekent dat ik van min 6 naar plus oneindig ga.","19dee9cf-1da4-4132-9330-9959a5fdbc71",654640,"En plus 1 is dus een positieve factor voor de wortel.","5693391a-007b-4f6c-bb97-3efbeb00c835",651640,"Daar staat niks, maar er staat in principe dus plus 1.","8743b8c1-c04e-42df-b276-14a677bf1734",647640,"Vandaar dat ik hier in het geel zo'n lijntje heb getekend bij dat plusje.","1244441a-e5fd-4fea-a95a-d78693baf116",644640,"Dus ik moet gaan kijken welke factor staat er voor de wortel.","d9387961-b556-4085-9bc8-0c47f8f510ee",638640,"Maar dan moet ik nog even kijken, loopt het bereik van min 6 naar min oneindig of van min 6 naar plus oneindig?","119f6bbc-eff4-462e-8bd6-1d7000552387",634640,"Het randpunt, de i-coördinaat is min 6, dus dat is al iets.","01bd85c4-ad20-4879-8859-99ed1fa44961",631640,"Wat betekent dat nu voor het bereik?","2e57b5cb-f03b-49a8-a25a-6c111dc030c9",626640,"Als ik in de functie van f op de plek van x 2 invul, dan komt daar min 6 uit.","affd2084-4db9-4483-814d-51ebd3c1be1d",623640,"Dus min 6 plus 0 kan ik direct invullen.","eed99017-64a8-457e-8bd7-6fc8b2a998ad",621640,"Want dat heb ik net met die ongelijkheid uitgerekend.","870323ff-2c5b-44da-bf07-b90bea9bac3b",617640,"Als ik die in de wortel invul, dan weet ik dat daar dus 0 uitkomt.","8ad68bf2-29bb-457b-9fac-7fe8afdbf594",614640,"De x-coördinaat van het randpunt is dus die 2 die we net gevonden hebben.","f3a6984c-c2ec-48eb-8f60-e87e9b3f6bfc",609640,"Om het bereik te bepalen moet ik dan weten wat de i-coördinaat van het randpunt is.","6e6c5020-fe65-4102-96f1-e827448c07bf",605640,"Dus die 2 rechts en dan naar min oneindig, pijltje naar links.","cd49f463-8b22-4dc0-bf68-11ddb9ea87ae",603640,"En daarna gaat hij naar min oneindig toe.","8670de19-a022-4f4a-984d-100cd8676cf9",597640,"Dus het domein, de hoogst mogelijke waarde van het domein is 2.","1083a1c7-9e25-4e8a-8a0b-09387e460d74",595640,"Min 10 gedeeld door min 5 is 2.","e7872611-a50e-45d8-a548-75ea4dde165e",592640,"Dus dan krijg ik x is kleiner of gelijk aan 2.","d0cf02c2-887a-488c-8fa2-b06497a990e9",589640,"Omdat min 5 negatief is, klapt het teken om.","e258b989-6961-45d4-99a4-d7218e06dccf",587640,"Vervolgens moet ik delen door min 5.","357801d7-9efc-4328-813a-aa6d39a1684c",582640,"Dan moet 10 naar links, dus dan krijg ik min 5x is groter of gelijk aan min 10.","daca353a-e982-4182-a095-d2a4c8e10b21",579640,"Wanneer is het groter of gelijk aan 0 om het domein te bepalen.","511111fa-081d-4e2f-bb77-c2f73a43ade7","En vervolgens gaan we kijken wat er in de wortel staat.","4938926b-0f34-41bc-a32d-72f6b7e8fa57",573640,"We noteren even de functie f.","fb6ed124-1a4a-4247-91d8-eea7fe7561fa",568640,"Geef het domein het bereik en de coördinaten van het randpunt van de grafiek van f.","54dd0d47-7875-4d96-b294-b0f10b714415",563640,"Gegeven is de functie fx is min 6 plus de wortel van 10, min 5x.","983ded67-794d-464c-bc99-dcefbc1e32ea",562239,"Opdracht 1a.","571eb2fd-e06f-4898-b37f-b67cca49f220",559239,"Dit gaan we gebruiken in de volgende opdrachten.","190b7b3d-b769-4293-a733-f55a83fddeb5",556239,558239,"Dus van min oneindig naar 0.","ee83cc10-a770-468f-922c-88adce9ca75d",552239,"En dan krijg je dat de hoogste waarde 0 is en dat die dan naar min oneindig gaat.","25ae83c8-903e-40ef-ac63-956fcf55e53e",548239,"Dan loopt de grafiek vanuit het randpunt naar links toe.","72b24116-67e5-4d97-b1b8-45ddbe3a9306",545239,"Zoals bij die groene en die paarse functie.","1f904ea7-d1c1-4bad-b3cc-e719d773e4f4",541239,"die x die in de wortel staat, staat daar een negatieve factor voor.","d82bf4c6-790b-4d82-ad61-6c978ec77959",537239,"Maar is b kleiner dan 0, dus staat er in de wortel,","b20164ef-c506-425e-8e15-836a2a4afd3c",534239,"Dus van 0 naar plus oneindig.","f646ab58-f367-4103-885a-644c8d069758",529239,"Dan is het domein van het randpunt naar rechts toe.","fbebb29e-b58e-4c7d-8de7-1fb292e9b508",525640,528640,"Dat is dus bij de blauwe en rode grafiek.","6b94430e-46d4-4b73-a44e-d4b328fc09d0",521640,"een positieve factor heeft voor zich.","d8c35880-fd70-4d3f-9187-44bf5064e113",516640,"Als b groter is dan 0, dus als de x die in de wortel staat,","59eee8bc-8786-4873-9168-1a179762ccb1",511640,"En die b, die bepaalt eigenlijk het verschil tussen het domein.","2617822e-61bb-4fb1-9bc8-f36eeee3317d",506640,509640,"Dus 0 is nu de hoogste waarde en vanuit daaruit ga ik naar beneden toe.","3052a16c-2734-4ede-9d58-6d667d1a041f",503640,"Dat betekent voor het bereik dat ik juist van min oneindig naar 0 ga.","e895965f-fac4-43ae-80e3-d4cecac5cebf",499040,503040,"Dan zie je dat ik vanuit het randpunt naar beneden toe ga.","2d673bda-55ba-4130-bc08-79279595a292",497040,"Dan, dat is dus die paars en die rode.","4fea037e-9beb-4640-8834-e8ecb759788e",492040,"En als a is kleiner dan 0, dus ik heb een negatieve wortel.","3c939398-1890-4d5f-8105-965e17a3564b",488040,"Dus het bereik is dan van 0 naar oneindig.","38a8bb46-d664-4c1f-a1fe-de6223cccdba",486040,"Dus ze starten in de oorsprong en dan gaan ze naar boven toe.","ee783cd8-b0c1-4108-9da3-ee3633606655",483040,"Dat maakt voor het bereik niet uit, het bereik is in de hoogte.","b0dcd036-cc7c-4b07-b36e-398dae0da6ad",481040,"De een wandel links en de ander naar rechts.","3ed76db7-7ead-4d39-bd70-3e21f2a77ebc",477040,"Nou het randpunt zit bij 0 en ze gaan daarna allebei naar boven toe.","fa2ec4c1-fc06-4afd-bbb9-50efd02d92ea",475040,"Want het bereik was de mogelijke eiwaarde.","5930c6ac-5d8f-4861-a1fd-d5a7c3d6b6cf",469440,474440,"Het bereik is in beide gevallen van 0 tot plus oneindig.","c0d8b588-d43d-47a7-9d9f-ca3a9b68b1c3",464440,467440,"Wat betekent dit voor het bereik en het domein?","cc57573a-68a9-43f3-b656-476319ac2049",461440,"Met de groene en de blauwe grafiek.","c87d79a6-346b-4449-95c1-422cd1f5bcbb",458440,"Dan heb ik dus te maken met de groene en de blauwe formule.","92fa4e34-29ea-4d4d-b26b-51fda6418438",457440,"a groter dan 0.","58879a8f-e347-4fde-b524-f1686e30ada2",453440,"Dus a is groter dan 0, dus de wortel aan de buitenkant is dus positief.","2ddd7b51-0fd2-4e7c-98b7-da26a70f7fae",449440,"Dus als ik nu eens ga kijken als a groter is dan 0.","0284c49d-2099-448e-ad65-249286a15229",447440,"En dan kan ik dit plaatje mooi bijgebruiken.","0a4b78fc-fb84-44c8-8b20-886c72f5b09e",439839,446839,"wat als ik met a positief of negatief of met b positief of negatief, wat gebeurt er dan?","9c10a301-58dd-4ab5-ae9c-c52910780aad",436839,"En nu kan ik vanuit deze functie gaan kijken","71106b85-2866-4875-832f-cf5f751d44dc",433839,"Nou dit ziet er al redelijk basic uit.","6110facc-c575-448d-a7d9-eac6946c27e3",428839,"Dus dan krijg je heel eenvoudig i is a wortel bx.","47a52ab4-c804-4aac-849e-304e83e9582b",425839,"Geen verticale translatie is vandaar dat die d ook 0 is.","f9a2798e-7bfe-4d72-a2fa-3498ad4187c8",420839,"Dus geen horizontale verplaatsing is vandaar dat die c 0 is.","0a6c5299-cef7-4439-b19d-adf6f2da2b5b",417839,"De beginpunt zit gewoon in de oorsprong.","484ee1f1-17db-4455-883f-1059ec3a122e",414239,"En voor d ook, want er is geen translatie.","67bf71ce-c14d-4bc9-b2c7-f6d2db563e30",408239,"Maar als ik nu naar deze varianten kijk, dan heb ik in ieder geval voor c 0 gekozen.","75ffbf87-d17c-4513-9b8a-54a0194b84cf",404239,"I is a keer de wortel van bx min c plus d.","0fbf76c7-e489-4d6d-8ebd-1026651258f5",401239,"Of ja, helemaal standaard is die natuurlijk niet.","8ebcd3de-056d-49af-95f2-9dd268628272",396239,"Nou heb ik hier dus een standaard wortelfunctie.","73260526-957d-408d-b4e2-92f95454cbad",391239,394239,"Van de functie i is wortel min x.","ed6c5141-e0cb-4e8e-bb73-c5210fbfdc4d",388239,"Maar dan van die groene functie.","e2a7fcd6-fa43-45cf-950e-e4a3e478b00f",380640,387640,"En die min buiten de wortel is dus in feite weer een spiegeling in de x-as.","ff6c3104-8536-497b-a798-ffee41e48b0b",376640,"Dus zowel een min buiten de wortel als een min binnen de wortel.","268d8e04-27c5-4d80-8aba-0257cd128052",373640,"En dan hebben we nog een paarse, i is min wortel min x.","45f8e2dd-2433-4112-8644-dd3b851f0b38",370640,"Dus niet bij x is 1 maar bij x is min 1.","8eb8deba-b372-40ae-b2e8-2cfce4ab9693",367640,"En voor die groene is het precies andersom.","f274b468-9ce9-43af-86f8-637e037ebf47",363640,"Dus bij x is 1, bij de blauwe zitten we op i is 1.","a98c473b-2395-443f-a076-feca98e5bc20",360640,"Ja, dat zien we inderdaad.","335c21e4-6795-4c88-83c2-18737a55213b",354040,360040,"En als je die groene grafiek nu vergelijkt met die blauwe, dan zie je als het ware dat dit een spiegeling is in de i-as.","8cc5016f-fc52-4424-bf81-00a85be19ad6",351040,"Omdat die alleen maar negatieve waarden voor x kan hebben.","06660103-0c18-41b5-bf33-d466651a713b",348040,"Maar dat de grafiek nu vanaf het randpunt naar links toe gaat.","5c770061-b21d-42b7-881d-390c39fc552a",345040,"Dus vandaar ook dat het randpunt nog steeds 0,0 is.","8bcee918-f83c-4cd1-bfe1-5912de4b9eb9",342040,"En voor de rest kan ik alleen maar negatieve waarden nu voor x invullen.","6a829f5c-fc96-4dec-9786-002311b4bb50",340040,"Dus wortel 0 kan natuurlijk ook.","aefb841d-2dbc-478a-a32e-aaab08a851bc",337040,"Nou, en als x is 0 dan krijg je natuurlijk min 0 is gewoon 0.","f2059805-50ae-4769-911f-99a0a9f61ef5","Maar wanneer wordt dat positief? Op het moment dat x een negatief getal is.","1c2f971f-2d26-449a-bf9e-915bc3d6c70c",331040,"Nu staat daar een min.","77dade35-2a4c-4cb3-ad1e-9455bb3d9fc5",327440,330440,"Maar je weet, je kunt geen negatief getal in de wortel invullen.","6b3d162c-5eba-46d4-ba0b-34d2db015fcd",325440,"De wortel van min x.","8e4f50a1-8864-4443-9f2a-9517153cd321","Dus nu staat het minnetje niet buiten de wortel, maar binnen de wortel.","4ccfac6e-8218-4f2c-ac92-68cd3989d3d4",316440,"Dan kijken we namelijk ook nog even naar de groene grafiek, i is de wortel van min x.","4f4183d3-2c6a-430c-ad88-ebb7213629a3","Dat gaan we zo bekijken.","190ac24c-db09-4e01-a48b-27b7e5858da5",308440,"Dat betekent natuurlijk het een en ander voor wellicht het domein of het bereik.","78eaee57-ede7-4f45-b4dd-bc7f2cfad9f8",303440,"En we hebben eerder al gezien, bij een vermenigvuldiging van min 1 wordt er gespiegeld in de x's.","8330818b-e90b-4938-be03-117dd67e8ca2",295839,302839,"Bij i is min wortel x is er een vermenigvuldiging ten opzichte van de x's van min 1 plaatsgevonden.","38c3e243-1bf2-4f33-a36f-e0038fe3e350",289839,"En die gaan we vergelijken met een paar andere, met bijvoorbeeld i is min wortel x.","acfc8d21-235a-417c-878a-d63fa0eb7fb4",284839,"Dus het randpunt zit in de oorsprong, i is wortel x.","09a95904-aba3-4457-81da-aa7a93b4e748",280839,"Er zijn geen vermenigvuldigen en geen translaties aan te pas gekomen.","17fa5b59-283e-4460-a6c4-cec31d3a9b2e",274839,"Nou gaan we, i is wortel x, dat is dus de meest eenvoudige wortelfunctie.","f49e400d-4e5e-4878-bcf2-4df39306fa38",267239,274239,"En als we hem dan tekenen, dan krijg je dus een wortelfunctie die nu vanaf zijn randpunt naar links toe omhoog loopt.","71ac1704-99c2-46c8-b77a-cc2181bf4542",263239,"Nou, dan gaan we hem nog even tekenen, dus ik heb hier de tabel van f.","096523db-9464-4ce3-aa8e-9c837dcae937",257239,261239,"maar van min oneindig naar je randpunt.","893fcfdb-3e27-4791-aeed-f91ed83633c3",250240,"Dus op het moment dat je een negatieve x krijgt, gaat dus het domein niet meer van laag naar hoog, naar plus oneindig,","2312fbb1-b07d-47e5-8647-0890831560b5",243639,249639,"Aan de rechterkant krijg je de hoogste waarde, dat is dus nu niet een pijl naar rechts, plus oneindig, maar dat is dus die 2,5.","13d1a0b1-0517-40bb-a245-5bb85931749a",238639,"Dus aan de linkerkant krijg je nu de laagste waarde, dat is dus min oneindig, dus de pijl naar links.","88435de3-cc31-437c-b10a-4fd84c6eda58",234639,"Dus vandaar dat we nu noteren dat de pijl naar links gaat.","b296fad7-1735-494b-a192-a19b35d6027c",229639,"En dat hij daarna dus alleen maar naar links toe kan, kleinig.","f62e4f68-d54c-475e-bb2e-a84ecd93a6cb",226039,"Dus dat betekent dat de hoogst mogelijke waarde van x 2,5 is.","05c3b58c-09ce-468f-a121-064843b1f3da",221639,"En er staat nu, x kan alleen maar kleiner of gelijk zijn dan 2,5.","98e6a002-e1ae-4d6c-8c47-11df078dcdcc",217839,"Het domein is dus de x-coördinaat van het randpunt.","b8282e27-4b18-4e72-bfee-4d0444d5e305",215839,"En het domein?","8c05cdb6-890a-428d-a4e2-df993a2c354a",211839,"En dat is dan dus de i-coördinaat van het randpunt.","e56ba5fd-5117-4da5-938d-5bab4434221e",209240,"Dus min 3 plus 0 is min 3.","0811330a-b7e8-4558-8105-409e016fabe2",204440,"Dan kun je gewoon meteen zeggen, oké, ik weet dat wat er in de wortel staat nu 0 is bij 2,5.","7cf707d1-bb2a-4477-8650-3637aecee064",201839,"Dus eigenlijk hoef je die berekening helemaal niet meer te doen.","702a912d-ef10-42cf-9f26-96dfdda1d156","En dat is natuurlijk logisch, want je hebt net gekeken wanneer er 0 uit 5 min 2x komt.","89649e0a-a64d-402f-9662-e3821db8160f",194240,"Dus 5 min 5 is de wortel van 0.","6126578e-d9dd-4f09-a6c6-1677fc620141",191240,"Maar goed, dan krijg je de wortel van 5 min 2x2,5.","82d3ad75-8fe3-4a7e-912c-fc7b299e935e",189039,"Nou, dan ga je die 2,5 invullen.","af710fd2-fd36-4cdb-b4d0-74b2ebeb0594",186639,"En wat is dan de i-coördinaat van het randpunt?","7a73605c-ce73-47d7-9796-332cf5a1ff6a",184639,"Dus daar zit het beginpunt.","c1ab3a58-ee1d-4779-ab7d-82a475747311",179639,"Het randpunt zit dan voor x op 2,5, want hij kan niet verder dan 2,5.","eb51f495-d370-4d49-bdad-d2105d3cbba6",178240,"Wat is het randpunt?","48e070ca-10f6-4178-a7de-fffc6c6e578b",176440,"Oh, we gaan eerst even naar het randpunt kijken.","28433784-3278-4507-9407-4fe61fcdd3c1",174240,"En dat maakt dat het domein van f...","9f7b0436-16f7-4e09-9889-3be3f169abe1",168440,"Dus de mogelijke x-waarden die er zijn is 2,5 en kleiner.","06713282-4d56-4c8e-b6e7-2dbce0d57fe8",165039,"Min 5 gedeeld door min 2 is 2,5.","d0c20498-0ea5-401d-81ac-96044d27c9fe",160839,"Dus dan krijg ik x niet meer groter dan of gelijk aan, maar kleiner dan of gelijk aan.","b04af10b-e276-4de3-bf82-1601dfad50b5",155039,"En omdat die 2 dus negatief is, betekent dat dat dat teken omklapt.","e8ee9f88-dc36-4d1b-bc26-be6d239b94fe",152639,"En vervolgens moeten we delen door min 2.","47349d36-c70c-438f-8390-504836f95e1b",149639,"Dus we hebben daar die 5 staan, die halen we naar links, min 5.","bed04fdc-659e-46a8-87f2-d22708e6cc52",148240,"Nou, dan gaan we x vrijmaken.","acb79c9f-2e01-411d-b703-572cbd5ba2d2",146839,"Voor welke x is dat?","d9006b9f-5d04-45b0-bc5b-112f8d59899b",142639,"Dus 5 min 2x moet groter of gelijk zijn dan 0, dan komt het goed.","e0db5ee4-3c73-4ddf-a403-99faf4b0e190",139039,142440,"Want de wortel van 0 kan natuurlijk wel, de wortel van 0 is 0.","897f0ab8-9aaa-487c-b37c-8a9c64e86fe6",132240,"In de wortel staat 5 min 2x en we moeten dus bedenken dat dat groter moet zijn of gelijk aan 0.","556efc51-4435-46c3-be15-d0333d217b74",130039,"De wortel van een negatief getal bestaat niet.","a939662a-3be4-4945-8bf4-041207c4385b",125639,"Je moet je dan realiseren dat je in de wortel geen negatief getal kunt invullen.","abcfde9a-52a4-4f26-b69e-8ac6f15e0e2f",117440,"Om het domein van f te bekijken, dan wil je dus weten wat zijn de mogelijke x-waarden die er allemaal zijn.","bb23725b-0e9c-40ff-a979-b6c2058f2826",115440,"Wat is dan het domein van f?","4275d9a6-0a26-411f-82f6-bdc9084b323e",109639,115239,"Dus je zet een factor voor die x die niet meer 1 is, maar 2 en negatief.","8cfd2108-43de-4444-83d6-e51b891be384",106440,"waarbij het niet meer 1x is, maar in dit geval zelfs min 2x.","1c86deec-2657-437a-a033-93d35bcd2e1f",102639,"Dus nu zien we voor het eerst in de wortel een x staan,","f8a37344-9e93-417f-8066-da1e6223fbdf",97239,"Gegeven is de functie fx is min 3 plus de wortel van 5 min 2x.","75527850-59e6-48b2-9b88-b8ebabb69a30",93440,"En we gaan nu eens even bekijken wat de invloed daarvan is.","c7b1533d-d39f-4351-9b86-92e6c6557e5f",90839,"2x, of misschien wel een negatieve waarde.","16f8addf-05e5-4d2a-9103-0a7d666ade37",86839,"En we hebben eigenlijk nog niet meegemaakt dat er een extra factor voor die x staat,","043e02dd-7b70-43f6-90a2-b8817c8aa6ac",82599,"En in die wortel hier ook zie je gewoon 1x.","2ee7b709-2a91-4f35-a36e-73b8091c77ba",78720,"net zoals hier in die wortel staat x en dat is dus 1x.","cfe4cd06-c292-4404-ab91-0a7be1c4e409",77199,"Wat we tot nu toe iedere keer gezien hebben,","f0d6b162-d629-4d65-a428-08761ebf1ea6",71519,"daar staat plus q, is dan ook positief q.","e2368da6-1d82-4107-8d72-d62e77c12f55",69919,"En de i-coördinaat van het randpunt,","5fba89a0-aac1-4d6b-8673-6d4dc0cfbffd",66599,"er staat min p, dus de x-coördinaat is p.","26bf2252-2b91-4e2c-a451-d0e0be9cdcb7",64599,"bij die, welke term staat er bij die x,","250af4ca-d83c-44a5-b09c-26c68b397895",62400,"als er, dan ga je kijken wat staat er,","f9cbb737-6f61-45de-84a4-2a797dee7f4d",59720,"dan kun je zeggen dat het randpunt,","bf951cb1-483f-46fd-b40c-ee3e5cf1af0a",57119,"zoals in het geval van f,","12ec2e9b-d6c8-4b08-ae56-e0da467b5160",55320,"Als de wortelfunctie van deze vorm is,","c856a931-2082-4c43-a107-67cafb30689b",49200,"Wortelfunctie van de vorm i is a keer de wortel van x min p plus q.","f973dfe4-4983-4a4f-8802-9e6f340899d6",45320,"dan komt die er als volgt uit te zien.","25dc9fc6-c757-495c-a573-36d38bce5858",42320,"En als we dan een schets zouden maken van deze functie,","a4bf85f5-4032-4c26-9f12-abfaa9751bf5",39119,"dus de i-coördinaat van het randpunt is min 4.","4e1035db-c0a5-4e7c-85eb-27762b2fee31",35880,"En buiten de wortel staat een losse term min 4,","537ac480-7bcd-42e1-8127-041ecd38a934","dus dat betekent dat de x-coördinaat van het randpunt min 3 is.","ca86a001-d42c-433c-9bf4-78671b63a7dc","de-grafiek-van-een-wortelfunctie","metaTitle","De grafiek van een wortelfunctie | Wiskunde B | Havo Vwo","metaDescription","In deze les leer je hoe je de grafiek van een wortelfunctie kunt tekenen en hoe je het randpunt kunt berekenen. Met video, Samenvatting en 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Veelgestelde vragen over De grafiek van een wortelfunctie

Alle vragen