Transform the given function f(x) as described and write the resulting function as an equation

Question

asked Nov 23, 2023 54.6k views

1 Answer

Gahrae · Answer 1 · 2023-11-29T21:34:05+0000

The given equation,

$f(x)=\sqrt[]{x}$

First it is horizontally stretched by a factor of 2.

$f(x)=\sqrt[]{2x}$

Then it is refected along y-axis,

$f(x)=\sqrt[]{-2x}$

It is then translated up by 2 unit.

$f(x)=\sqrt[]{-2x}+2$

Thus the resulting function becomes as:

$y=\sqrt[]{-2x}+2\Rightarrow y-2=\sqrt[]{-2x}$

Squaring both side,

$y^2-4y+4=-2x\Rightarrow y^2+2x-4y+4=0$

Thus the required equation is: