Chapter 6, Problem 19CR

To determine

To describe : the transformation of $f$ represented by $g$ and graph the function

Answer to Problem 19CR

The graph of $g$ is horizontal transformation 5 units left and a vertical stretch by a factor by $\frac{1}{2}$ of the graph of $f$

Explanation of Solution

Given information$f\left(x\right)={\log }_{4}x$ , $g\left(x\right)=\frac{1}{2}{\log }_4\left(x+5\right)$

Notice that the function is of the form $g\left(x\right)=a{\log }_4\left(x-h\right)$ . Where $a=\frac{1}{2}$ and $h=-5$

So, the graph of $g$ is horizontal transformation 5 units left and a vertical stretch by a factor by $\frac{1}{2}$ of the graph of $f$

  

Hence, the graph of $g$ is horizontal transformation 5 units left and a vertical stretch by a factor by $\frac{1}{2}$ of the graph of $f$