Chapter 7.6, Problem 26PPS

To determine

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

Answer to Problem 26PPS

The graph of $g\left(x\right)={11}^{x+2}+8$ is sifted $2-unit$ in the negative $x-axis$ and $6-unit$ in positive $y-axis$ respectively.

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)={11}^{x+2}+8$

Since $g\left(x\right)={11}^{x+2}+8$ so let the parent function is $p\left(x\right)={11}^x$

By added $"2"$ in exponential part and added $"8"$ in non-exponential part of parent function $p\left(x\right)={11}^x$ then $g\left(x\right)={11}^{x+2}+8$ is arrived

So, by the concept of translation of graph when something is added in exponential part of the parent function then the graph is shifted in the negative $x-axis$ and also when something in non-exponential part of parent function then the graph is shifted in positive $y-axis$ respectively.

So, the graph of $g\left(x\right)={11}^{x+2}+8$ is sifted $2-unit$ in the negative $x-axis$ and $6-unit$ in positive $y-axis$ respectively.