Chapter 7.6, Problem 65HP

To determine

To explain how reflection about x -axis affects each points on the graph of an exponential function.

Explanation of Solution

Let an exponential function be assumed: $y=f(x)=2^x$

Taking reflection about x -axis: $y=-f(x)=-2^x$

Calculation for graph:

Consider $y=f(x)=2^x$

Values of x	Values of f (x)
0	1
1	2
-1	0.5
2	4
3	8

From the above table the graph can be plotted.

Calculation for graph:

Consider $y=-f(x)=-2^x$

Values of x	Values of f (x)
0	-1
1	-2
-1	-0.5
2	-4
3	-8

From the above table the graph can be plotted.

Plotting both the graphs on the same plane:

  

Interpretation:

From the above graph, it is clear that, all the values of positive values of y will change to negative values of y after taking reflection about x -axis.