Chapter 2, Problem 58RE

To determine

To sketch: the graph of the function. Also state the domain, intercepts and range of the graph.

Answer to Problem 58RE

The range is $\left\{y|y\ge 0\right\}$ .

Domain of function $g\left(x\right)=\frac{1}{2}\left|x\right|$ is the set of all real numbers.

Explanation of Solution

Given information:

Given function

  $g\left(x\right)=\frac{1}{2}\left|x\right|$

Calculation:

Let us consider the following function

  $g\left(x\right)=\frac{1}{2}\left|x\right|$

The function $g\left(x\right)=\frac{1}{2}\left|x\right|$ has the same shape as the graph of $f\left(x\right)=\left|x\right|$ .

The graph of $g\left(x\right)=\frac{1}{2}\left|x\right|$ is the vertically compressed by a factor of $\frac{1}{2}$ .

The graph $g\left(x\right)=\frac{1}{2}\left|x\right|$ is plotted below using Maple.

  

From the graph we see the domain of function $g\left(x\right)=\frac{1}{2}\left|x\right|$ is the set of all real numbers. We see $g\left(x\right)=\frac{1}{2}\left|x\right|$ can take any values greater than or equal to 0. Hence the range is $\left\{y|y\ge 0\right\}$