Question

Match the description with the correct Function.

Function A:

Function B:

x y
0 1
4 9
8 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

Options: Function A, Function B, Function C

Answer 1

Let's analyze each function and the given descriptions:

### Function A:
Points: (0, 1), (4, 9), (8, 17)

To find the rate of change, we can calculate the change in y over the change in x between the points:
- From (0, 1) to (4, 9):
- Change in y = 9 - 1 = 8
- Change in x = 4 - 0 = 4
- Rate of change = 8 / 4 = 2

- From (4, 9) to (8, 17):
- Change in y = 17 - 9 = 8
- Change in x = 8 - 4 = 4
- Rate of change = 8 / 4 = 2

Overall, the rate of change for Function A is consistent at 2.

### Function B:
The data points are not provided, but we can look for y-intercept indirectly via the descriptions mentioned.

### Function C:
Given by the equation \(y = x + 20\)
- The y-intercept is 20 (when x=0).

### Description Analysis:
- **Function with the greatest rate of change**:
- Function A has a constant rate of change of 2.
- We would need the information for Function B to compare, but based on Function C, it has a rate of change of 1. Without Function B's data, we can't conclude definitely, but Function A appears to have a higher rate than Function C.

- **Function with the smallest y-intercept**:
- Function A has a y-intercept of 1. Function C has a y-intercept of 20. The smallest y-intercept we may find is from the unprovided Function B.

- **Which function would benefit you the most if it represented your money earned per hour?**:
- Function A has a consistent rate of earnings, and if Function B were taken into account and provided better data concerning a higher rate, we'd need that comparison. Function C offers a static addition to the earnings (1 per hour starting from 20).

- **Function with the highest initial amount of money**:
- Function C has a starting amount of 20 (y-intercept); Function A has a starting point of 1.

### Conclusion:
Assuming Function B has lower or comparable data based on available information, we can summarize:

- **Function with the greatest rate of change**: Function A (or potentially Function B if provided and better)
- **Function with the smallest y-intercept**: Function A (assuming Function B has a y-intercept > 1)
- **Which function would benefit you the most if it represented your money earned per hour?**: Function A (due to its rate of growth).
- **Function with the highest initial amount of money**: Function C.

Thus:

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