Chapter 9.2, Problem 61PS

To determine

(a)

To graph:

The functions $f\left(x\right)=\left|x\right|$, $f\left(x\right)=2\left|x\right|$, $f\left(x\right)=4\left|x\right|$, and $f\left(x\right)=\frac{1}{2}\left|x\right|$ on the same set of axes.

To determine

(b)

To graph:

The functions $f\left(x\right)=\left|x\right|$, $f\left(x\right)=-\left|x\right|$, $f\left(x\right)=-3\left|x\right|$, and $f\left(x\right)=-\frac{1}{2}\left|x\right|$ on the same set of axes.

To determine

(c)

To conjecture:

The graphs of $f\left(x\right)=a\left|x\right|$, here $a$ is a nonzero real number from the results of parts (a) and (b).

To determine

(d)

To graph:

The functions $f\left(x\right)=\left|x\right|$, $f\left(x\right)=\left|x\right|+3$, $f\left(x\right)=\left|x\right|-4$, and $f\left(x\right)=\left|x\right|+1$ on the same set of axes and to make a conjecture about the graphs of $f\left(x\right)=\left|x\right|+k$, here $k$ is a nonzero real number.

To determine

(e)

To graph:

The functions $f\left(x\right)=\left|x\right|$, $f\left(x\right)=\left|x-3\right|$, $f\left(x\right)=\left|x-1\right|$, and $f\left(x\right)=\left|x+4\right|$ on the same set of axes and to make a conjecture about the graphs of $f\left(x\right)=\left|x-h\right|$, here $h$ is a nonzero real number.

To determine

(f)

To sketch:

The graphs of the given functions and use a graphing calculator to check these sketches.