Chapter 4.6, Problem 22PPE

To determine

To calculate: Domain and range of the function $d(x)=32x$

Answer to Problem 22PPE

Domain is $\left[0,17\right]$

Range is $\left[0,544\right]$

Explanation of Solution

Given information: A car can travel 32 mi for each gallon of gasoline. The function $d(x)=32x$ represents the distance $d(x)$ in miles that the car can travel with $x$ gallons of gasoline.

Calculation:

Domain refers to all the input values that go into a function.

The range refers to all the output values of the given function for the given input values.

Given function is $d(x)=32x$

The car’s fuel tank holds 17 gallons.

So,

  $0\le x\le 17$

Domain is $\left[0,17\right]$

Multiply both sides of $0\le x\le 17$ by $32$

  $\begin{array}{l}0\times 32\le 32x\le 17\times 32\\ 0\le 32x\le 544\end{array}$

So,

Range is $\left[0,544\right]$

Now find the points that can be used to plot the graph of $d(x)=32x$

  $\begin{array}{l}x=0;d(x)=32(0)=0\\ x=1;d(x)=32(1)=32\\ x=2;d(x)=32(2)=64\\ x=-1;d(x)=32(-1)=-32\\ x=-2;d(x)=32(-2)=-64\end{array}$

x	0	1	2	$-1$	$-2$
y	0	32	64	$-32$	$-64$