The amount a basketball coach spends at a sporting goods store depends on the number of basketballs the coach buys. The situation is represented by the function rule a=16b

Question

Make a table of values and graph the function rule. Is the graph continuous or​ discrete? Explain.
Suppose the coach spent 112​$ before tax. How many basketballs did she​ buy?

Answer 1

To create a table of values for the function rule a=16b, we can assign different values to b and then calculate the corresponding values of a.

| b | a |
|---|---|
| 1 | 16 |
| 2 | 32 |
| 3 | 48 |
| 4 | 64 |
| 5 | 80 |

To graph the function, we can plot the points (b,a) on a coordinate plane. The x-axis represents the number of basketballs (b) and the y-axis represents the amount spent (a).

The graph of the function rule is a straight line passing through the origin (0,0) with a slope of 16.

The graph is continuous because it does not have any breaks or jumps. It consists of all possible values of a, which are the multiples of 16.

To find the number of basketballs the coach bought if she spent $112, we can substitute a=112 into the function and solve for b:

112 = 16b

Dividing both sides by 16 gives:

b = 112/16

b = 7

Therefore, the coach bought 7 basketballs.