Question

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

Answer 1

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:

`y^2+2x-4y+4=0`