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 aequals
16
b.
a.
Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain.
b.
Suppose the coach spent $128
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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(Simplify your answers.)
The function rule is given as \( a = 16b \), where \( a \) represents the amount of money the coach spends, and \( b \) represents the number of basketballs purchased. It is implied that each basketball costs $16.
Let's fill in the table:
\( b \) | \( a \)
---|---
0 | \( 16 \times 0 = 0 \)
1 | \( 16 \times 1 = 16 \)
2 | \( 16 \times 2 = 32 \)
3 | \( 16 \times 3 = 48 \)
4 | \( 16 \times 4 = 64 \)
For graphing the function rule:
If you graph the rule \( a = 16b \) on a Cartesian plane with \( b \) on the x-axis and \( a \) on the y-axis, you would plot the points (0,0), (1,16), (2,32), (3,48), and (4,64). Connect the dots with a straight line, and you'll find a linear graph. However, because a basketball coach cannot buy a fraction of a basketball, the graph would be a set of discrete points rather than a continuous line, with points representing only whole numbers of basketballs.
To plot the points:
- Start at the origin (0,0).
- Move 1 unit to the right along the x-axis and 16 units up along the y-axis; place a point at (1,16).
- Move another unit to the right and another 16 units up to place a point at (2,32).
- Continue this pattern to plot the other points.
Is the graph continuous or discrete?
The graph of the function rule is discrete because we are dealing with a scenario in which the variable \( b \) (the number of basketballs) can only take on whole number values. You cannot buy 1.5 basketballs, for instance, so the graph would consist of isolated points at each whole number value of \( b \).
Part 2:
For the second part of the question, we want to determine how many basketballs the coach bought if she spent $128 before tax.
We use the function rule \( a = 16b \) and substitute \( a \) with $128.
\( 128 = 16b \)
Now we need to solve for \( b \):
\( b = \frac{128}{16} \)
\( b = 8 \)
Thus, the coach bought 8 basketballs.