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fazlası için: http://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3183910/195de20e0c0b5c0b11531ea1a31175ba/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/_oXgRAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"8","reqid":"1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL&text=videoid:1310005414626168234","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik eğitim içeriğidir. Bir eğitmen, öğrencilere fonksiyon grafiği sorusunu adım adım çözmektedir.","Videoda, f(x) = g(x) / (x² - x - 6) fonksiyonunun grafiği sorulmaktadır. Eğitmen önce paydayı çarpanlarına ayırarak paydayı sıfır yapan değerleri (x = 3 ve x = -2) bulur, ardından bu değerlerin fonksiyonun grafiğinde dikey asimptot veya kaldırılabilir süreksizlik oluşturduğunu açıklar. Dört seçenek arasından doğru grafiği bulmak için her seçeneği inceleyerek, C seçeneğinin doğru olduğunu gösterir."]},"endTime":277,"title":"Matematik Dersinde Fonksiyon Grafiği Sorusu Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Fonksiyonun Analizi","list":{"type":"unordered","items":["Soruda f(x) = g(x) / (x² - x - 6) fonksiyonunda g(x)'in bir polinom olduğu verilmiş ve hangi grafik f(x)'in grafiği olabilir sorulmuş.","Paydanın sıfır yapan x değerleri bulunarak, bu noktalarda dikey asimptot veya kaldırılabilir süreksizlik olabileceği incelenecek.","Payda çarpanlarına ayrılarak (x-3)(x+2) şeklinde ifade edilmiş ve paydayı sıfır yapan değerler x=3 ve x=-2 olarak bulunmuş."]},"beginTime":0,"endTime":100,"href":"/video/preview/1310005414626168234?parent-reqid=1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL&text=FifthFunction&t=0&ask_summarization=1"},{"index":1,"title":"Asimptotların Analizi","list":{"type":"unordered","items":["Paydanın herhangi bir noktada sıfır olması, o noktada ya bir dikey asimptot ya da kaldırılabilir süreksizlik olacağı anlamına gelir.","x=3'te kaldırılabilir süreksizlik olması için g(x)'in çarpanlarından birinin x-3 olması gerekir.","Eğer g(3) veya g(-2) sıfıra eşit değilse, bu noktalar dikey asimptot olur."]},"beginTime":100,"endTime":130,"href":"/video/preview/1310005414626168234?parent-reqid=1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL&text=FifthFunction&t=100&ask_summarization=1"},{"index":2,"title":"Seçeneklerin İncelenmesi","list":{"type":"unordered","items":["A seçeneğinde x=-2 noktasında dikey asimptot var ancak x=3 noktasında tanımlı olduğu için yanlış.","B seçeneğinde x=2 ve x=4'te iki dikey asimptot var, bu da mantıklı değil çünkü f(x) x=3'te tanımlı ve sıfıra eşit.","C seçeneğinde x=-2'de dikey asimptot ve x=3'te kaldırılabilir süreksizlik var, bu da doğru görünüyor.","D seçeneğinde x=-1 ve x=6'da iki dikey asimptot var ancak bunların ikisi de paydayı sıfır yapmadığı için yanlış."]},"beginTime":130,"endTime":273,"href":"/video/preview/1310005414626168234?parent-reqid=1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL&text=FifthFunction&t=130&ask_summarization=1"}],"linkTemplate":"/video/preview/1310005414626168234?parent-reqid=1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL&text=FifthFunction&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Rasyonel Fonksiyonların Grafikleri: Dikey Asimptotlar 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fazlası için: http://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1005708/ef963d8126877154f34e2d609e8b8aeb/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/0hry0gAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"9","reqid":"1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL&text=videoid:17398397510884854108","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik eğitim içeriğidir. Bir eğitmen, rasyonel fonksiyonların grafiklerini bulma konusunda bir soru çözümü sunmaktadır.","Videoda, f(x) = 2x² - 18/g(x) şeklinde tanımlanan bir rasyonel fonksiyonun grafiği hangi seçeneklerden biri olabileceği sorusu ele alınmaktadır. Eğitmen, payın çarpanlara ayrılması, dikey asimptotlar ve kaldırılabilir süreksizlikler gibi kavramları açıklamakta ve seçenekleri tek tek incelemektedir. Sonuç olarak, doğru cevabın A seçeneği olduğu gösterilmektedir."]},"endTime":456,"title":"Rasyonel Fonksiyonun Grafiği Bulma Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Rasyonel Fonksiyonun Tanımlanması","list":{"type":"unordered","items":["Soruda f(x) = 2x² - 18 / g(x) şeklinde tanımlanan bir rasyonel fonksiyon verilmiş ve g(x) bir polinom olarak belirtilmiştir.","Sorunun amacı, y = f(x) grafiğinin hangi seçenekle eşleştiğini bulmaktır.","Çözüm için f(x) fonksiyonunun tanımına bakarak grafiklerden hangisinin ona ait olduğunu belirlemek gerekmektedir."]},"beginTime":0,"endTime":49,"href":"/video/preview/17398397510884854108?parent-reqid=1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL&text=FifthFunction&t=0&ask_summarization=1"},{"index":1,"title":"Payın Çarpanlarına Ayırılması","list":{"type":"unordered","items":["Payın çarpanlarına ayrılması yapılarak f(x) = 2(x² - 9) / g(x) şeklinde ifade edilmiştir.","x² - 9 ifadesi kareler farkı olarak (x + 3)(x - 3) şeklinde yazılabilir.","Payın sıfıra eşit olduğu durumlar x = -3 ve x = 3 değerlerinde gerçekleşir."]},"beginTime":49,"endTime":133,"href":"/video/preview/17398397510884854108?parent-reqid=1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL&text=FifthFunction&t=49&ask_summarization=1"},{"index":2,"title":"Seçeneklerin İncelenmesi","list":{"type":"unordered","items":["A seçeneğinde x = 3 değerinde bir değer var ancak x = -3 değerinde ilgi çekici bir durum yoktur.","B seçeneğinde x = 3'te bir değer var ancak x = -3 için tanımlı dikey asimptotu bile yoktur.","C seçeneğinde x = 3'te sürekli değil ve dikey asimptotu x = -2'dedir.","D seçeneğinde fonksiyonun sıfır olduğu iki değer var ancak bunlar x = -3 ve x = 3 değil, x = -6 ve x = 6'dır."]},"beginTime":133,"endTime":181,"href":"/video/preview/17398397510884854108?parent-reqid=1774800847669674-6521659584431409627-balancer-l7leveler-kubr-yp-klg-18-BAL&text=FifthFunction&t=133&ask_summarization=1"},{"index":3,"title":"Payı Sıfır Yapan Değerlerin Anlamı","list":{"type":"unordered","items":["Payı sıfır yapan değerlerin fonksiyonun da sıfır olacağı anlamına gelmediği vurgulanmıştır.","Örneğin, g(x) = x + 1 olduğunda, payı sıfır yapan değerler (x = -3 ve x = 3) fonksiyonun sıfır olduğu noktalardır.","Payı sıfır yapan değerlerden biri fonksiyon için kaldırılabilir süreksizlik anlamına gelebilir.","Payı sıfır yapan değerler fonksiyonun sıfır olduğu, kaldırılabilir süreksizlik olduğu veya dikey asimptot olduğu durumları 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Relax! It's just Functions! 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