Chapter 7.6, Problem 17PPS

To determine

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

Answer to Problem 17PPS

The graph of $g\left(x\right)={\left(\frac{9}{5}\right)}^{x-2}$ is sifted $2-unit$ in positive $x-axis$ .

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)={\left(\frac{9}{5}\right)}^{x-2}$

Since $g\left(x\right)={\left(\frac{9}{5}\right)}^{x-2}$ so let the parent function is $p\left(x\right)={\left(\frac{9}{5}\right)}^x$

By subtracting $"2"$ in the exponential part of parent function $p\left(x\right)={\left(\frac{9}{5}\right)}^x$ then $g\left(x\right)={\left(\frac{9}{5}\right)}^{x-2}$ is arrived

So, by the concept of translation of graph when something is subtracting in the exponential part of parent function then the graph is shifted in positive $x-axis$ .

So, the graph of $g\left(x\right)={\left(\frac{9}{5}\right)}^{x-2}$ is sifted $2-unit$ in positive $x-axis$ .