Chapter 7.6, Problem 47PPS

To determine

To use the transformation to graph the given function

Explanation of Solution

Given:

  $y={\left(\frac{1}{4}\right)}^{x+2}-2$

Hence, the parent function will be: $y={\left(\frac{1}{4}\right)}^x$

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 $y={\left(\frac{1}{4}\right)}^x$

Values of x	Values of y
0	1
-1	4
1	0.25
-2	16
2	0.5

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

Graph:

  

Step 2: Now shift the obtained graph 2 units to the left horizontally.

  

Step 3: Now vertically shift the obtained graph 2 units downward.

  

Conclusion:

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