Chapter 8.3, Problem 66HP

To determine

To Explain: The process of graphing the transformation.

Answer to Problem 66HP

First draw the graph of ${\log }_{10}x$

Then translate the graph

Explanation of Solution

Given: A transformation of ${\log }_{10}x$ is $g(x)=a{\log }_{10}(x-h)+k$

Given: ${\log }_{10}x$

First draw the graph of ${\log }_{10}x$

Then for the random values of $a,h,k$

Translate the graph

As

If $\left|a\right|>1$ the graph expands vertically, If $\left|a\right|<1$ the graph compressed vertically

  $h=0$ there is no horizontal shift

If $h<0$

The graph is translated $h$ units to left.

If $h>0$

The graph is translated $h$ units to right.

If $k$ is negative

The graph is translated $k$ units to down.

If $k$ is positive

The graph is translated $k$ units to up.