Chapter 4.4, Problem 3P

a.

To determine

To graph: The function $w=3t$

Explanation of Solution

Given information: The amount of water $w$ in a wading pool, in gallons, depends on the amount of time $t$ , in minutes, the wading pool has been filling, as related by the function rule $w=3t$

Graph:

First find some points that can be used to draw the graph.

At $t=0,w=3(0)=0$

At $t=1,w=3(1)=3$

At $t=2,w=3(3)=6$

At $t=-1,w=3(-1)=-3$

At $t=-2,w=3(-2)=-6$

Plot points $(0,0),\text{}(1,3),(2,6),(-1,-3),(-2,-6)$

  

Interpretation:

If all the points of the graph are connected by a single line then the graph is said to be continuous. If the points are not connected by a single line then the graph is discrete.

As the graph of $w=3t$ is connected by a single line, the graph is continuous.

b.

To determine

To graph: The function $C=16n$

Explanation of Solution

Given information:The cost $C$ for basketball tickets, in dollars, depends on the number $n$ of tickets bought, as related by the function rule $C=16n$

Graph:

First find some points that can be used to draw the graph.

At $t=0,C=16(0)=0$

At $t=\frac{1}{2},C=16\left(\frac{1}{2}\right)=8$

At $t=\frac{-1}{2},C=16\left(\frac{-1}{2}\right)=-8$

At $t=1,C=16\left(1\right)=16$

At $t=-1,C=16\left(-1\right)=-16$

Plot the points $(0,0),\left(\frac{1}{2},8\right),\left(\frac{-1}{2},-8\right),\left(1,16\right),\left(-1,-16\right)$

  

Interpretation:

If all the points of the graph are connected by a single line then the graph is said to be continuous. If the points are not connected by a single line then the graph is discrete.

As the graph of $C=16n$ is connected by a single line, the graph is continuous.