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)
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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

Answer 1

To match the descriptions with the correct functions, let's first analyze each function:

**Function A (the table):**
- It gives points (0, 1), (4, 9), and (8, 17).

To find the rate of change for Function A, we can calculate the differences:
- 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, Function A has a constant rate of change of 2.

**Function B (not provided, assumed to be Function A):**
- We did not analyze Function B since it is not defined in the context, but we will assume it is the table as there is no further information.

**Function C:**
- y = x + 20
- The y-intercept is 20 when x = 0, and the rate of change of Function C is 1.

Now let's answer the questions:

1. **Function with the greatest rate of change**:
- Function A has a rate of change of 2, Function C has a rate of change of 1.
- **Answer: Function A**

2. **Function with the smallest y-intercept**:
- For Function A, at x=0, y=1 (the y-intercept is 1).
- For Function C, the y-intercept is 20.
- **Answer: Function A** (since 1 < 20)

3. **Which function would benefit you the most if it represented your money earned per hour?**:
- Function A has a higher constant rate of change (2), suggesting it could represent a higher earning rate compared to Function C.
- **Answer: Function A**

4. **Function with the highest initial amount of money**:
- The initial amount for Function A (at x=0) is 1, and for Function C (at x=0) is 20.
- **Answer: Function C**

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