Asosiy tarkibga o'tish

4.6-bo'lim : Transformatsiyalar

4. Quyidagi funksiyaning grafigini chizish uchun transformatsiyalardan foydalaning.

\[f\left( x \right) = {\left( {x - 5} \right)^2}\]
Yechim

Avval “tayanch” funksiyasini aniqlaymiz (i.e. biz o'zgartirayotgan funktsiya). Bu holda biz \(g\left( x \right) = {x^2}\) ni o'zgartirayotganga o'xshaymiz.

2-qadam

Bu erda mavjud funktsiyani quyidagicha yozish mumkin:

\[f\left( x \right) = {\left( {x - 5} \right)^2} = g\left( {x - 5} \right)\]

Shunday qilib, biz \(f\left( x \right)\) grafigi shunchaki 5 ga o'ngga siljigan \(g\left( x \right)\) 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 \(g\left( x \right) = {x^2}\), the blue dashed curve, and \(f\left( x \right) = {\left( {x - 5} \right)^2}\), the red solid curve. Both are upward opening parabolas of exactly the same shape, but the vertex of the dashed parabola is at the origin while the vertex of the solid parabola has been shifted 5 units to the right to \(\left( {5,0} \right)\).