Chapter 1.2, Problem 70E

To determine

To graph: $g(x)=\left|4x-21\right|$

Explanation of Solution

Graph:

First find points that can be used to draw the graph

At $x=0,g(x)=\left|4(0)-21\right|=21$

At $x=1,g(x)=\left|4(1)-21\right|=17$

At $x=-1,g(x)=\left|4(-1)-21\right|=\left|-4-21\right|=25$

At $x=2,g(x)=\left|4(2)-21\right|=\left|8-21\right|=13$

At $x=-2,g(x)=\left|4(-2)-21\right|=\left|-8-21\right|=29$

At $x=\frac{21}{4},g(x)=\left|4\left(\frac{21}{4}\right)-21\right|=\left|21-21\right|=0$

Now plot the points $(0,21),(1,17),(-1,25),(2,13),\left(-2,29\right),\left(\frac{21}{4},0\right)$ and join them

  

From the graph it can be observed that domain is $\left(-\infty ,\infty \right)$ and range is $[0,\infty )$ .