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.
a.
Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain.
b.
Suppose the coach spent $112 before tax. How many basketballs did she buy?
a. To create a table of values, we can substitute different values for 'b' (the number of basketballs) and calculate the corresponding value of 'a' (the amount spent).
| Number of basketballs (b) | Amount spent (a) |
|-------------------------|-----------------|
| 0 | 0 |
| 1 | 16 |
| 2 | 32 |
| 3 | 48 |
| 4 | 64 |
To graph the function rule, we can plot the points (0, 0), (1, 16), (2, 32), (3, 48), (4, 64) on a coordinate plane and draw a line connecting them. The graph of the function rule is a straight line.
The graph is continuous as there are no breaks or jumps in the line. It smoothly extends in both directions.
b. We have the equation a = 16b and know the amount spent is $112. Substituting this into the equation:
112 = 16b
Dividing both sides by 16:
b = 7
Therefore, the coach bought 7 basketballs.