Question

What transformations are needed in order to obtain the graph of G(x) from the graph of F(x)? Select all that apply

Answer 1

ANSWER and EXPLANATION

We want to identify the transformations that were made in obtaining:

`g(x)=-|x-4|-2`

from:

`f(x)=|x|`

When a function is transformed by:

`g(x)\to-f(x)`

It implies that there is a reflection across the x-axis.

When a function is transformed by:

`g(x)\to f(x)-k`

It implies that there is a vertical shift downwards by k units.

When a function is transformed by:

`g(x)\to f(x-h)`

it implies that there is a horizontal shift to the right by h units.

Therefore, for the given function, the transformations made are:

* Vertical shift

* Horizontal shift

* Reflection about the x-axis.