Question

g(x)=|-2x|-3 Describe the transformations from f(x) = |x| to g(x)

Answer 1

Given the Parent Function (the simplest form) of Absolute Value Functions:

$f\mleft(x\mright)=|x|$

And the function obtained after the transformation:

$g\mleft(x\mright)=|-2x|-3$

You need to remember the following Transformation Rules for Functions:

1. If:

$f(x)-k$

The function is shifted down "k" units.

2. If:

$f(-x)$

The function is reflected across the y-axis.

See the graph attach below:

Where the green function is the Parent Function and the purple function is the function g(x).

By definition, for Absolute Value functions, when the transformation is:

$f(x)=a|x|$

and:

$a>1$

The graph is stretched.

Therefore, you can determine that the answer is:

-Translation of 3 units down.

- Reflection across the y-axis.

- Stretched by a scale factor of:

$a=2$