Chapter 7.6, Problem 51PPS

To determine

To use the transformation to graph the given function

Explanation of Solution

Given:

  $y={\left(\frac{2}{3}\right)}^{4x}$

Hence, the parent function will be: $y={\left(\frac{2}{3}\right)}^x$

To use the transform to graph the given function, the following steps have to be followed.

Step 1: Graph the parent function.

Calculation for graph:

Consider $y={\left(\frac{2}{3}\right)}^x$

Values of x	Values of y
0	1
-1	1.5
1	0.67
-2	2.25
2	1.33

By taking different values of x , the graph can be plotted.

Graph:

  

Step 2: Now horizontally shrink the obtained graph 4 times.

  

Conclusion:

So, by following the steps the graph of the given function can be transformed.