Chapter 7.6, Problem 49PPS

To determine

To use the transformation to graph the given function

Explanation of Solution

Given:

  $y=-0.5{(4)}^{x-3}+1$

Hence, the parent function will be: $y=4^x$

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 $y=4^x$

Values of x	Values of y
0	1
-1	0.25
1	4
2	16
3	64

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

Graph:

  

Step 2: Now vertically shrink the obtained graph 0.5 times.

  

Step 3: Now take the reflection of the obtained graph about x -axis.

  

Step 4: Then, horizontally shift the obtained graph 3 units to the right.

  

Step 5: Then, vertically shift the obtained graph 1 units upward.

  

Conclusion:

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