Question

18.

Function A: Function B: Function C: y=x+5

(4 points)
a. Which function has the greatest rate of change (slope)?

b. Which function has the smallest y-intercept?

c. Which function would you want to represent your money earned per hour?

d. Which function would give you the highest initial amount of money?

Answer 1

To answer your questions regarding Functions A, B, and C given that Function C is y = x + 5, we need to establish the information about Functions A and B. Since we only have the details for Function C, I will make some assumptions about Functions A and B. Below, I will answer each inquiry based on typical behaviors for linear functions.

### Given Information:
Function C: \( y = x + 5 \)
- This function has a slope (rate of change) of \( 1 \) and a y-intercept of \( 5 \).

### General Analysis:
- The slope of a function indicates its rate of change. The steeper the slope, the greater the rate of change.
- The y-intercept is the value of \( y \) when \( x = 0 \).
- A function that represents money earned per hour should have a positive slope (meaning you earn more money as time increases).
- The initial amount of money might be represented by the y-intercept.

However, without specific definitions for Functions A and B, here's how to approach each question hypothetically:

### a. Which function has the greatest rate of change (slope)?
If Function A has a slope greater than 1 and Function B has a slope less than 1, then:
- **The function with the greatest slope (rate of change) among A, B, and C would be determined by their respective slopes.**

### b. Which function has the smallest y-intercept?
- **If Function A has a y-intercept less than 5 and Function B has a y-intercept more than 5, then Function A would have the smallest y-intercept.**

### c. Which function would you want to represent your money earned per hour?
- Typically, **the function with the highest positive slope** represents the most money earned per hour. If either Function A or B has a slope greater than that of C (1), then that function would be preferable.

### d. Which function would give you the highest initial amount of money?
- **The function with the highest y-intercept** will provide the greatest initial amount of money. If Function A has a y-intercept greater than 5 and Function B has a y-intercept lower than 5, then Function A would give you the most money initially.

### Conclusion
Unfortunately, without explicit details about Functions A and B, we cannot definitively answer the questions. If you provide the equations or data for Functions A and B, I would be more than happy to analyze them!