Question

Match the description with the correct Function.
(8, 0)
-5
10
Function A:
(4, - 1)
(0, -2)
Function B:
0
4
1
9
17
Function C: y = x + 20
(4 points)
Function with the greatest rate of change
Function with the smallest y-intercept
Which function would benefit you the most if it represented your money earned per hour?
Function with the highest initial amount of money
:: Function A
:: Function B
:: Function C

Answer 1

To match the descriptions with the correct functions, we need to analyze each function based on the provided points and equations.

### Functions:

1. **Function A:**
- Points: (8, 0), (4, -1), (0, -2)
- To find the rate of change, we can use the points:
- From (0, -2) to (8, 0):
\[
\text{Rate of change} = \frac{0 - (-2)}{8 - 0} = \frac{2}{8} = \frac{1}{4}
\]

2. **Function B:**
- Points: (0, 0), (1, 4), (9, 10), (17, ?)
- Since we only have starting points (initial amount) and sample calculations could be done from the line segments available.
- It's implied that function B starts at (0, 0) which is a y-intercept of 0.

3. **Function C:**
- Equation: \(y = x + 20\)
- The y-intercept is 20 (when \(x = 0\)).

### Analyzing the functions based on descriptions:

1. **Function with the greatest rate of change:**
- We need to compare the rates of change. We only calculated the rate for Function A and didn't calculate the exact rates for B and C's line segments specifically, but since Function C has a constant change of 1 (from y = x + 20) and B could have variable changes, we can say for sure C has a constant rate of change.
- Here it seems like Function C probably has the most consistent increase.

2. **Function with the smallest y-intercept:**
- Function A: y-intercept is -2.
- Function B: y-intercept is 0.
- Function C: y-intercept is 20.
- Therefore, Function A has the smallest y-intercept.

3. **Which function would benefit you the most if it represented your money earned per hour:**
- Function A gives negative earnings in certain ranges.
- Function B has a y-intercept of 0, suggesting you would earn some money only after spending some hours (initial earning).
- Function C has the highest y-intercept at 20, strongly suggesting a favorable rate of earnings.

4. **Function with the highest initial amount of money:**
- Function C: y-intercept = 20 (highest).
- Function B: 0 (starting).
- Function A: -2 (negative starting).

### Final Matching:

- **Function with the greatest rate of change:** Function C
- **Function with the smallest y-intercept:** Function A
- **Which function would benefit you the most if it represented your money earned per hour?:** Function C
- **Function with the highest initial amount of money:** Function C

So the most suitable matches are:
1. Greatest rate of change: **Function C**
2. Smallest y-intercept: **Function A**
3. Benefit most if representing money: **Function C**
4. Highest initial amount: **Function C**

**Final answers are:**
- Function with the greatest rate of change: **Function C**
- Function with the smallest y-intercept: **Function A**
- Benefit the most: **Function C**
- Highest initial amount: **Function C**