Chapter 3.8, Problem 63PFA

To determine

To determine the translation in the graph of the given function $g(x)=\left|x\right|+1.3$ .

Answer to Problem 63PFA

Up, (C)

Explanation of Solution

Given:

Function: $g(x)=\left|x\right|+1.3$

Concept used:

The general form of an absolute value function is $f(x)=a\left|x-h\right|+k$ .

The vertex of the function is $\left(h,k\right)$ .

The variables $h$ and $k$ tell how far the graph shifts horizontally and vertically.

The graph opens up if $a>0$ and opens down if $a<0$ . If $0<a<1$ , the graph is compressed, and if $a>1$ , it is stretched.

The graph of $f(x)=\left|x\right|$ is translated $h$ units horizontally and $k$ units vertically to get the graph of $f(x)=a\left|x-h\right|+k$ .

Calculation:

Consider the function $g(x)=\left|x\right|+1.3,$

Comparing with the general form $g(x)=a\left|x-h\right|+k.$

Here, $a=1$ , $h=0$ and $k=\mathrm{1.3.}$

Since $k=1.3$ , the graph of the parent function $f(x)=\left|x\right|$ is translated $\left(1.3\right)$ units up.

Conclusion:

Therefore, the graph of the parent function $f(x)=\left|x\right|$ is translated $\left(1.3\right)$ units up.

Option (C) is correct.