Question

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 $a = 14b$
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. complete the following table of values
(simplify your answers )

Explanation:

Step1: Calculate a for b=0

Substitute $b=0$ into $a=14b$:
$a=14\times0=0$

Step2: Calculate a for b=1

Substitute $b=1$ into $a=14b$:
$a=14\times1=14$

Step3: Calculate a for b=2

Substitute $b=2$ into $a=14b$:
$a=14\times2=28$

Step4: Calculate a for b=3

Substitute $b=3$ into $a=14b$:
$a=14\times3=42$

Step5: Calculate a for b=4

Substitute $b=4$ into $a=14b$:
$a=14\times4=56$

Step6: Analyze graph type

You can only buy whole number basketballs, so the graph is discrete (points only, no connected line, since non-integer values of b don't make sense here).

Step7: Solve for b when a=112

Set $a=112$ in $a=14b$, solve for $b$:
$112=14b$
$b=\frac{112}{14}=8$

Answer:

Completed Table:

b	0	1	2	3	4

Part a Graph Analysis:

The graph is discrete. You cannot buy a fraction of a basketball, so only whole-number values of $b$ (number of basketballs) are valid, meaning the graph consists of separate points, not a continuous line.

Part b:

8 basketballs