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=17b.
a.
Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain.
b.
Suppose the coach spent $102 before tax. How many basketballs did she buy?
a. To make a table of values, we can assign different values to the variable b (the number of basketballs bought) and then calculate the corresponding value of a (the amount spent at the sporting goods store). Let's choose a range of values for b:
b = 0: a = 17(0) = 0
b = 1: a = 17(1) = 17
b = 2: a = 17(2) = 34
b = 3: a = 17(3) = 51
b = 4: a = 17(4) = 68
Using these values, we can create a table:
b | a
--------
0 | 0
1 | 17
2 | 34
3 | 51
4 | 68
Now let's graph the function rule. On the x-axis, we have the number of basketballs bought (b), and on the y-axis, we have the amount spent (a). We plot the points from the table:
(0, 0), (1, 17), (2, 34), (3, 51), (4, 68)
Connecting these points, we get a straight line that passes through all the points. The graph of this function rule is continuous.
b. Let's solve the equation a = 17b for b when a = $102:
102 = 17b
Dividing both sides by 17:
102/17 = b
Approximately:
b ≈ 6
So, the coach bought approximately 6 basketballs.