Asosiy tarkibga o'tish

4.6-bo'lim : Transformatsiyalar

6. Quyidagi funksiya grafigini chizish uchun transformatsiyalardan foydalaning.

\[f\left( x \right) = \sqrt {x + 4} - 3\]
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:

\[f\left( x \right) = \sqrt {x + 4} - 3 = g\left( {x + 4} \right) - 3\]

Shunday qilib, biz \(f\left( x \right)\) grafigi shunchaki 4 ga chapga va 3 ga pastga siljigan \(g\left( x \right)\) ning 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 \(f\left( x \right) = \sqrt {x + 4} - 3\), the red solid curve. Both curves have the same shape but the solid curve has been shifted 4 units to the left and 3 units down, so it starts at \(\left( { - 4, - 3} \right)\) instead of the origin.