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!
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