Chapter 7.6, Problem 4AGP

To determine

Find the translation of the function.

Answer to Problem 4AGP

The graph of $g\left(x\right)=2^{-0.25x}$ shows reflection with respect to $y-axis$ and bent away from the $y-axis$ .

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)=2^{-0.25x}$

Since $g\left(x\right)=2^{-0.25x}$ so let the parent function be $f\left(x\right)=2^x$

By multiplying $"-0.25"$ to the exponential part of $f\left(x\right)$ then $g\left(x\right)=2^{-0.25x}$ is arrived

So, by the concept of translation of graph when something negative quantity is multiplying in to the exponential part of function which is $"<1"$ then the graph shows reflection and bent away to the $y-axis$ .

So, the graph of $g\left(x\right)=2^{-0.25x}$ shows reflection with respect to $y-axis$ and bent away from the $y-axis$ .