Chapter 4.6, Problem 14P

Find a reasonable domain and range for each function. Then graph the function.

A charter boat travels at a maximum rate of 25 miles per hour. The function $d(x)=25x$ represents the distance $d(x),$ in miles, that the boat can travel in $x$ hours. The charter boat travels a maximum distance of 75 miles from the shore.

To determine

The range and domain of given function and also plot the graph.

Answer to Problem 14P

Domain = $x\in \left[0,3\right]$ .

Range= $d(x)\in \left[0,75\right]$ .

  

Explanation of Solution

Given:

The function $d(x)=25x$ ,where $d(x)$ represents the distance in miles.

The charter boat travels a maximum distance of $75$ miles from the shore.

A charter boat travels at a maximum rate of $25$ miles per hour.

Since $d(x)=25x$ and maximum $d(x)=75$

So $x=\frac{75}{25}$

Thus $x=3\text{hours}$

Domain = $x\in \left[0,3\right]$ ,as time is always positive.

Range= $d(x)\in \left[0,75\right]$

Now the graph is shown below;