Chapter 3.8, Problem 48PPS

To determine

To compress the graph of the given function $f(x)=-4\left|x\right|-3$ vertically by a factor of $\frac{1}{4}$ .

Answer to Problem 48PPS

  $f(x)=-\left|x\right|-\frac{3}{4}$

Explanation of Solution

Given:

Function: $f(x)=-4\left|x\right|-3$

Concept used:

The vertical compression is the squeezing of the graph toward the $x$ -axis.

The graph of $y=a\cdot f(x)$ is vertically compressed if $0<a<1$ , by multiplying each of its $y$ coordinates by $a$ .

Calculation:

Consider the function $f(x)=-4\left|x\right|-3$ .

Since it needs to be compressedvertically by a factor of $\frac{1}{4}$ ,

  $\Rightarrow a=\frac{1}{4}$

The function $f(x)$ after compression becomes:

  $\begin{array}{l}f(x)=a\cdot f(x)\\ \Rightarrow f(x)=\frac{1}{4}\left(-4\left|x\right|-3\right)\\ \Rightarrow f(x)=-\left|x\right|-\frac{3}{4}\end{array}$

Conclusion:

Therefore, the function $f(x)$ after translation is $f(x)=-\left|x\right|-\frac{3}{4}.$