Chapter 7.6, Problem 30PPS

To determine

Find the translation of the given function relates to its parent function.

Answer to Problem 30PPS

The graph of $g\left(x\right)=-5^{x-8}+4$ shows reflection with respect to $x-axis$ , shifted $8-unit$ in the direction of positive $x-axis$ and shifted $4-unit$ in the direction of positive $y-axis$

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)=-5^{x-8}+4$

Since $g\left(x\right)=-5^{x-8}+4$ so let the parent function is $p\left(x\right)=5^x$

By multiplying $"-1"$ , subtracting $"8"$ in the exponential part and adding $"4"$ in non-exponential part of $p\left(x\right)$ then $g\left(x\right)=-5^{x-8}+4$ is arrived

So, by the concept of translation of graph when something negative quantity is multiplying in the function then the graph shows reflection with respect to $x-axis$ , subtracting in the exponential part then the graph shifted in the direction of positive $x-axis$ and adding in non-exponential part then the graph shifted in the direction of positive $y-axis$ .

So, the graph of $g\left(x\right)=-5^{x-8}+4$ shows reflection with respect to $x-axis$ , shifted $8-unit$ in the direction of positive $x-axis$ and shifted $4-unit$ in the direction of positive $y-axis$ .