Chapter 8.3, Problem 51PPS

To determine

To Graph: The function.

Answer to Problem 51PPS

  

Explanation of Solution

Given: $f(x)=4{\log }_2(2x-4)+6$

Given: $f(x)=4{\log }_2(2x-4)+6$

Transform the given function

  $\begin{array}{l}f(x)=4{\log }_2(2x-4)+6\\ =4({\log }_2(2(x-2))+6\\ =4({\log }_{2}2+{\log }_2(x-2))+6\\ =4+4{\log }_2(x-2)+6\\ =4{\log }_2(x-2)+10\end{array}$

Thus

  $f(x)=4{\log }_2(x-2)+10$

The graph of the function is

  

This shows the transformation of the function ${\log }_{2}x$

  $\left|a\right|=4$ : The graph is expands vertically

  $h=2$ : The graph is translated $2$ units to the right.

  $k=10$ : The graph is translated $10$ units to the up.