Chapter C, Problem 1ES

To determine

To sketch: the graph of the given function.

Explanation of Solution

Given information:

The given functionis $f\left(x\right)=3\left|x\right|$ .

Concept used:

Let graph of $f\left(x\right)=a\left|x-h\right|+k$ .

Has vertex $\left(h,k\right)$ and is $\text{V}$ shaped.

Opens upward if $a>0$ and downward if $a<0$ .

If $\left|a\right|<1$ , the graph is wider than the graph of $y=\left|x\right|$ .

If $\left|a\right|>1$ , the graph is narrower than the graph of $y=\left|x\right|$ .

Consider the given function.

  $f\left(x\right)=3\left|x\right|$

Compare the given graph to general form of the graph.

Then, $a=3$ and $\left(h,k\right)=\left(0,0\right)$ .

The required function is shown in figure $\left(1\right)$ .

 

Figure $\left(1\right)$

Since, $a>0$ , then the graph opens upward with vertices $\left(0,0\right)$ .

Therefore, the required function is shown in figure $\left(1\right)$ .