Chapter 6.1, Problem 26E

To determine

To graph: the given function and to compare with the parent function and then to

describe the domain and range.

Explanation of Solution

Given information:

The given equation is $f(x)=-4^x$

Concept used:

Domain is the set of input values for which the function is defined.

Range is the set of output values for input values which are in domain.

Calculation:

Make a table of values for $f(x)=-4^x$

$x$	$-6$	$-1$	$0$	$1$	$1.6$
$f(x)$	$0$	$-0.25$	$-1$	$-0.25$	$-9.9$

The graph of $f(x)=-4^x$ is shown below.

  

The parent function of given function is $y=4^x$

The graph of $y=-4^x$ and its parent function is shown below.

  

Hence,

The graph of $y=-4^x$ is the reflection of the graph of the parent function across x-axis..

Domain is $(-\infty ,\infty )$ , Range is $(-\infty ,0)$