Chapter 1.5, Problem 8E

To determine

To sketch: The graphs of the function $y=e^x,y=e^{-x},y=8^x\text{ and }y=8^{-x}$ on the same axes and interpret how these graphs are related.

Explanation of Solution

The rough graphs of the functions $y=e^x,y=e^{-x},y=8^x\text{ and }y=8^{-x}$ are drawn and shown below in Figure 1.

From Figure 1, it is observed that the graphs of the functions are passing through the common point (0, 1) as the value of $e^0$ is always 1.

Also, notice that the functions $y=e^x\text{ and }y=8^x$ approaches $\infty$ as x tending to $\infty$ and approaches 0 as x tending to $-\infty$ as they have the positive exponents. Therefore, the graphs are monotonically increasing.

Similarly, the functions $y=e^{-x}\text{ and }y=8^{-x}$ approaches 0 as x tending to $\infty$ and approaches $\infty$ as x tending to $-\infty$ as they have the positive exponents. Therefore, the graphs are monotonically decreasing.