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 analyze the functions A, B, and C, we need to know their specific equations to answer your questions. You've provided Function C, which is \( y = x + 5 \). Without the equations of Functions A and B, I will use hypothetical functions for illustration. Let's say:

- Function A: \( y = 2x + 3 \)
- Function B: \( y = 0.5x - 2 \)
- Function C: \( y = x + 5 \)

With these examples, we can answer your questions:

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

The slopes for the hypothetical functions are:
- Function A: slope = 2
- Function B: slope = 0.5
- Function C: slope = 1

Function A has the greatest rate of change (slope of 2).

b. **Which function has the smallest y-intercept?**

The y-intercepts for the hypothetical functions are:
- Function A: y-intercept = 3
- Function B: y-intercept = -2
- Function C: y-intercept = 5

Function B has the smallest y-intercept (-2).

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

Generally, you'd want a function with a positive and high slope to represent money earned per hour, indicating a higher rate of income. Here, Function A (slope of 2) would be preferred.

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

The highest initial amount is indicated by the y-intercept. Here are the y-intercepts:
- Function A: 3
- Function B: -2
- Function C: 5

Function C has the highest initial amount of money (y-intercept of 5).

### Summary with Hypothetical Functions:
- **Greatest rate of change (slope):** Function A
- **Smallest y-intercept:** Function B
- **Best for money earned per hour:** Function A
- **Highest initial amount of money:** Function C

If you provide the specific equations for Functions A and B, I can give you precise answers based on those functions!