Question

Describe how the graph of each function differs from the graph of f(x)=|x|. Then determine the domain and range.

Answer 1

A. We can compress the graph of the function $f(x)=|x|$ in the y-direction by multiplying the whole function by a constant C, such that $0$ Since $0$, the graph of the function $g(x)= 0.6|x|$ is obtained from the graph of the function  $f(x)=|x|$ by compression in the y-direction.

B. We can stretch the graph of the function $f(x)=|x|$ in the y-direction by multiplying the whole function by a constant C, such that $C>1.$ Since $4>1,$, the graph of the function $g(x)= 4|x-3|$ is obtained from the graph of the function  $f(x)=|x|$ by compression in the y-direction and translation 3 units to the right.

C. We can flip the graph of the function  $f(x)=|x|$ upside down by multiplying the whole function by −1, then translate 1 unit to the left and 5 units up. Then we will get the function $g(x)=-|x+1|+5.$