Chapter 1.3, Problem 20E

To determine

To sketch: The function $y=\left|x\right|$ by hand without plotting any points and then graph of the function $y=\left|x\right|-2$.

Explanation of Solution

The standard graph of the function $y=\left|x\right|$ is roughly drawn as shown below in Figure 1.

Then, draw the graph of $y=\left|x\right|-2$ by shifting the graph $y=\left|x\right|$ by 2 units downward. Thus, the graph of $y=\left|x\right|-2$ is shown below in Figure 2.

Observe that Figure 2 is obtained from Figure 1 in such a way that it is shifted downward by 2 units.