Question

# g is related to one of the parent functions Describe the sequence of transformations from f to g. g(x) = 1/2|x - 2| - 3

Transformations of functions

g is related to one of the parent functions Describe the sequence of transformations from f to g.

$$g(x) = \frac{1}{2}|x - 2| - 3$$

2021-06-22

We are starting with the parent function $$f(x)=|x|$$
STEP 1:

Vertically compress the graph by a factor of $$\frac{1}{2}$$, to get $$y=\frac{1}{2}|x|$$
STEP 2:

Shift the graph by 2 units to the right, to get $$y=\frac{1}{2}|x-2|$$
STEP 3:

Shift the graph by 3 units downwards, to get $$y=\frac{1}{2}|x-2|-3$$, which is the required function g(x)