Asosiy tarkibga o'tish

4.6-bo'lim : Transformatsiyalar

1. Quyidagi funksiya grafigini chizish uchun transformatsiyalardan foydalaning.

\[f\left( x \right) = \sqrt x + 4\]
Yechim

Avval “tayanch” funksiyasini aniqlaymiz (i.e. biz o'zgartirayotgan funktsiya). Bu holda biz \(g\left( x \right) = \sqrt x \) ni o'zgartirayotganga o'xshaymiz.

2-qadam

Bu erda mavjud funktsiyani quyidagicha yozish mumkin:

\[f\left( x \right) = \sqrt x + 4 = g\left( x \right) + 4\]

Shunday qilib, biz \(f\left( x \right)\) ning grafigi shunchaki \(g\left( x \right)\) ning 4 ga siljigan grafigi bo'lishini ko'rishimiz mumkin.

3-qadam

Bu erda ikkala asosiy funktsiyaning (ko'k chiziqli egri chiziq) va bizdan grafik qilishimiz so'ralgan funktsiyaning (qizil qattiq egri) eskizi.

The graphs of the base function \(g\left( x \right) = \sqrt x \), the blue dashed curve, and \(f\left( x \right) = \sqrt x + 4\), the red solid curve. Both curves have the same shape, starting at the left and increasing while flattening out as they move to the right, but the solid curve sits 4 units above the dashed one and starts at \(\left( {0,4} \right)\) instead of the origin.