Chapter 11.2, Problem 124E

a.

To determine

To sketch: The graphs of $f\left(x\right)=2^x$ and $g\left(x\right)={\left(\frac{1}{2}\right)}^x$, and then conclude that the point $\left(1,2\right)$ is on the graph of $f$ and the point $\left(\_\_\_\_,2\right)$ is on the graph of $g$. Also, the point $\left(-1,\frac{1}{2}\right)$ is on the graph of $f$ and the point $\left(\_\_\_,\frac{1}{2}\right)$ is on the graph of $g$. Both graphs contain the point ________.

b.

To determine

To sketch: The graphs of $f\left(x\right)=3^x$ and $g\left(x\right)={\left(\frac{1}{3}\right)}^x$, and then conclude that the point $\left(1,3\right)$ is on the graph of $f$ and the point $\left(\_\_\_\_,3\right)$ is on the graph of $g$. Also, the point $\left(-1,\frac{1}{3}\right)$ is on the graph of $f$ and the point $\left(\_\_\_,\frac{1}{3}\right)$ is on the graph of $g$. Both graphs contain the point ________.

c.

To determine

To conclude: For the function $f\left(x\right)=a^x$ and $g\left(x\right)={\left(\frac{1}{a}\right)}^x$, where $a>1$, if the point $\left(1,a\right)$ is on the graph of $f$, the point $\left(\_\_\_\_,a\right)$ is on the graph of $g$; if the point $\left(\_\_\_,\frac{1}{a}\right)$ is on the graph of $f$, the point $\left(\_\_\_,\frac{1}{a}\right)$ is on the graph of $g$; both graphs contain the point ________.