Chapter 9, Problem 1RE

To determine

To Calculate: The graph for the function of the graph.

Answer to Problem 1RE

Solution:

The provided graph is a function $f\left(x\right)=4^{-x}$.

Explanation of Solution

Given:

Calculation:

The provided functions are $f\left(x\right)=4^x$,$f\left(x\right)=4^{-x}$,$f\left(x\right)=-4^{-x}$ and $f\left(x\right)=-4^{-x}+3$.

Study the provided graph carefully,

$x$	$f\left(x\right)=4^{-x}$	$4^{-x}$
$-2$	$4^{-(-2)}=4^2=16$	16
$-1$	$4^{-(-1)}=4^1=4$	4
$0$	$4^{-0}=1$	1
$1$	$4^{-1}=\frac{1}{4}$	$\frac{1}{4}$
$2$	$4^{-2}=\frac{1}{4^2}=\frac{1}{16}$	$\frac{1}{16}$

The provided graph is the resultant of the transformation on the graph oftheexponentialfunction $4^x$.

On studying the provided graph, it is concluded that the provided 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, then the graph of a function $4^{-x}$ is obtained.

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