Chapter 3, Problem 1RE

To determine

The function $g\left(x\right)=4^{-x}$ using the graph. The graphs are as follows:

Answer to Problem 1RE

Solution:

The correct graph of the given equation is $\underset{}{g\left(x\right)=4^{-x}}$ .

Explanation of Solution

Let us consider the functions are as follows:

(a). $f\left(x\right)=4^x$

(b). $g\left(x\right)=4^{-x}$

(c). $h\left(x\right)=-4^{-x}$

(d). $r\left(x\right)=-4^{-x}+3$.

And observe the given graph carefully.

Given below the graph is the resultant of the transformation on the graph of the exponential function $4^x$.

On observing the graph, it is concluded that the graph is a reflection of the graph of an exponential function $4^x$ about the y-axis.

If the graph of an exponential function $4^x$ is reflected about the y-axis in the graph, then obtain the graph of function $4^{-x}$ as follows:

Thus, the provided graph is of function $g\left(x\right)=4^{-x}$.