Asosiy tarkibga o'tish

4.6-bo'lim : Transformatsiyalar

7. Quyidagi funksiyaning grafigini chizish uchun transformatsiyalardan foydalaning.

\[f\left( x \right) = \left| {x - 7} \right| + 2\]
Yechim

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

2-qadam

Bu erda mavjud funktsiyani quyidagicha yozish mumkin:

\[f\left( x \right) = \left| {x - 7} \right| + 2 = g\left( {x - 7} \right) + 2\]

Shunday qilib, biz \(f\left( x \right)\) grafigi shunchaki \(g\left( x \right)\) ning 7 ga va 2 ga yuqoriga 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 \(g\left( x \right) = \left| x \right|\), the blue dashed curve, and \(f\left( x \right) = \left| {x - 7} \right| + 2\), the red solid curve. Both are “V” shaped graphs of exactly the same shape, but the point of the dashed “V” is at the origin while the point of the solid “V” has been shifted 7 units to the right and 2 units up to \(\left( {7,2} \right)\).