Chapter 3.8, Problem 12CYU

To determine

To graph the function $g(x)=\left|-2x\right|$ and states its domain and range and compare with function $f(x)=\left|x\right|$

Explanation of Solution

The graph of the function $g(x)=\left|-2x\right|$ is given as follows-

  

The domain of $g(x)=\left|-2x\right|$ is $\left(-\infty ,\infty \right)$ , that is all real numbers,

Because $x$ can take any real values.

The range of $g(x)=\left|-2x\right|$ is $\left(0,\infty \right)$ that is all positive real numbers only,

Because $g(x)$ can take only positive values.

The graph of function $f(x)=\left|x\right|$ is as follows-

  

Since there is factor of 2 with variable $x$ in the function $g(x)=\left|-2x\right|$ as compared to the function $f(x)=\left|x\right|$ . So the graph of $g(x)$ is shrinked 2 times as compared to $f(x)$ .