Chapter 8.7, Problem 6OE

To determine

To find: The range of the given function.

Answer to Problem 6OE

The range is $\left\{2,5\right\}$ .

Explanation of Solution

Given:

The given function is:

  $Q\left(n\right)=3n^3+2$

And the given domain is:

  $D=\left\{-1,0,1\right\}$

In order to find the range of the given function, replace $n$ with each member of the domain.

The table given below shows the corresponding value of $Q\left(n\right)$ after replacing $n$ with each member of the given domain is as:

Table1

$n$	$3n^2+2$
$-1$	$3{\left(-1\right)}^2+2=5$
$0$	$3{\left(0\right)}^2+2=2$
$1$	$3{\left(1\right)}^2+2=5$

So, the range of the given function is:

  $R=\left\{2,5\right\}$

Therefore, the range is $\left\{2,5\right\}$ .