Asosiy tarkibga o'tish

4.6-bo'lim : Transformatsiyalar

2. Quyidagi funksiya grafigini chizish uchun transformatsiyalardan foydalaning.

\[f\left( x \right) = {x^3} - 2\]
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:

\[f\left( x \right) = {x^3} - 2 = g\left( x \right) - 2\]

Shunday qilib, biz \(f\left( x \right)\) grafigi oddiygina \(g\left( x \right)\) ning 2 ga pastga 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 \(g\left( x \right) = {x^3}\), the blue dashed curve, and \(f\left( x \right) = {x^3} - 2\), the red solid curve. Both curves have the same shape, flattening out as they pass through their center point and rising steeply on either end, but the solid curve sits 2 units below the dashed one and flattens out at \(\left( {0, - 2} \right)\) instead of the origin.