The exercise involves understanding how the cost of basketballs varies with quantity, represented by the function $ a = 14b $, where $ a $ is the total amount spent and $ b $ is the number of basketballs purchased.### Tasks**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?**### Table Completion- **b (Number of Basketballs):** 0, 1, 2, 3, 4- **a (Amount Spent in $):** This part requires calculation using the function $ a = 14b $.### Completing the Table1. For $ b = 0 $, $ a = 14 \times 0 = 0 $.2. For $ b = 1 $, $ a = 14 \times 1 = 14 $.3. For $ b = 2 $, $ a = 14 \times 2 = 28 $.4. For $ b = 3 $, $ a = 14 \times 3 = 42 $.5. For $ b = 4 $, $ a = 14 \times 4 = 56 $.### Understanding the Graph- **Graph Type:** The graph is discrete because the number of basketballs (b) is a countable quantity (whole numbers only), not continuous.### Solving Part bFor a purchase amount of $112:- Set $ a = 112 $ in the equation $ a = 14b $.- Solve for $ b $: \[ 112 = 14b \implies b = \frac{112}{14} = 8 \]Therefore, the coach bought 8 basketballs.

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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. 2 3. 4 a (Simplify your answers.)

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. 2 3. 4 a (Simplify your answers.)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

The exercise involves understanding how the cost of basketballs varies with quantity, represented by the function $ a = 14b $, where $ a $ is the total amount spent and $ b $ is the number of basketballs purchased.

### Tasks

**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?**

### Table Completion

- **b (Number of Basketballs):** 0, 1, 2, 3, 4
- **a (Amount Spent in $):** This part requires calculation using the function $ a = 14b $.

### Completing the Table
1. For $ b = 0 $, $ a = 14 \times 0 = 0 $.
2. For $ b = 1 $, $ a = 14 \times 1 = 14 $.
3. For $ b = 2 $, $ a = 14 \times 2 = 28 $.
4. For $ b = 3 $, $ a = 14 \times 3 = 42 $.
5. For $ b = 4 $, $ a = 14 \times 4 = 56 $.

### Understanding the Graph
- **Graph Type:** The graph is discrete because the number of basketballs (b) is a countable quantity (whole numbers only), not continuous.

### Solving Part b
For a purchase amount of $112:
- Set $ a = 112 $ in the equation $ a = 14b $.
- Solve for $ b $:
\[
112 = 14b \implies b = \frac{112}{14} = 8
\]

Therefore, the coach bought 8 basketballs.

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