Asosiy tarkibga o'tish

4.6-bo'lim : Transformatsiyalar

5. Quyidagi funksiyaning grafigini chizish uchun transformatsiyalardan foydalaning.

\[f\left( x \right) = - {x^3}\]
Yechim

Avval “tayanch” funksiyasini aniqlaymiz (i.e. biz o'zgartirayotgan funktsiya). Bu holda biz \(g\left( x \right) = {x^3}\) ni o'zgartirayotganga o'xshaymiz.

2-qadam

Bu erda mavjud funktsiyani quyidagicha yozish mumkin:

\[f\left( x \right) = - {x^3} = - g\left( x \right)\]

Shunday qilib, biz \(f\left( x \right)\) grafigi shunchaki \(x\) o'qida aks ettirilgan \(g\left( x \right)\) 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 \(g\left( x \right) = {x^3}\), the blue dashed curve, and \(f\left( x \right) = - {x^3}\), the red solid curve. The solid curve is the dashed curve reflected about the x-axis, so the dashed curve rises from the lower left to the upper right while the solid curve falls from the upper left to the lower right. The two cross at the origin.