Chapter 6.3, Problem 28E

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 $f(x)=6{\left(\frac{1}{3}\right)}^x$

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 $f(x)=6{\left(\frac{1}{3}\right)}^x$

$x$	$-10$	$-1$	$0$	$1$	$1.2$
$f(x)$	$0$	$-0.286$	$-2$	$-14$	$-21$

The graph of $f(x)=6{\left(\frac{1}{3}\right)}^x$ is shown below.

  

The parent function of given function is $f(x)={\left(\frac{1}{3}\right)}^x$

The graph of $f(x)=6{\left(\frac{1}{3}\right)}^x$ and its parent function is shown below.

  

Hence,

The graph of $f(x)=6{\left(\frac{1}{3}\right)}^x$ is the vertical stretch by the factor $6$ of the graph of the parent function.

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