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
=
18b.
a.
Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain.
b.
Suppose the coach spent $
144 before tax. How many basketballs did she buy?
Question content area bottom
Part 1
a. Complete the following table of values.
b
0
1
2
3
4
a
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a.
0 - 0
1 - 18
2 - 36
3 - 54
4 - 72
b.
To graph the function rule, plot the points (0, 0), (1, 18), (2, 36), (3, 54), and (4, 72) on a coordinate system and connect the points with a straight line.
The graph of the function rule is a straight line.
The graph is continuous because the coach can buy any number of basketballs, including fractions or decimals. There are no gaps or interruptions in the graph.
b.
If the coach spent $144 before tax, we can use the function rule a = 18b to find the number of basketballs she bought.
144 = 18b
Divide both sides by 18 to isolate b:
b = 144/18
b = 8
Therefore, the coach bought 8 basketballs.
b. She bought
enter your response here basketballs.
b. She bought 8 basketballs.
To complete the table of values, we can use the given function rule a = 18b. By substituting the values for b into the function, we can find the corresponding values for a.
a. Complete the table of values:
b 0 1 2 3 4
a 0 18 36 54 72
To find the values for a, we substitute the values for b in the given function rule. For example, when b=0, we substitute b=0 into the function rule a = 18b, so a = 18(0) = 0. Similarly, for b=1, a=18(1)=18, for b=2, a=18(2)=36, and so on.
b. To find how many basketballs the coach bought when she spent $144 before tax, we can rearrange the given function rule to solve for b.
a = 18b
Divide both sides of the equation by 18:
a/18 = b
Substitute the value of a as $144:
144/18 = b
b = 8
Therefore, the coach bought 8 basketballs.