Question

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?

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Answer 1

To analyze the functions and answer your questions, we first need to determine the slopes and y-intercepts of the given functions. Since you provided only one function \(y = x + 5\) (Function C), I will assume that there are three functions, possibly some linear ones. To illustrate, let's assume:

- Function A: \(y = mx + b_A\)
- Function B: \(y = nx + b_B\)
- Function C: \(y = x + 5\) (This has a slope of 1 and a y-intercept of 5)

We will need to define Functions A and B if we're to genuinely analyze their properties. However, since you only provided Function C, I will analyze Function C against generic forms of Functions A and B with hypothetical slopes and intercepts.

Assuming more concrete examples, let's consider:

- Function A: \(y = 2x + 3\) (slope = 2, y-intercept = 3)
- Function B: \(y = 0.5x + 1\) (slope = 0.5, y-intercept = 1)
- Function C: \(y = x + 5\) (slope = 1, y-intercept = 5)

With these examples, we can answer the questions:

a. **Which function has the greatest rate of change (slope)?**
- Function A (slope = 2) has the greatest rate of change.

b. **Which function has the smallest y-intercept?**
- Function B (y-intercept = 1) has the smallest y-intercept.

c. **Which function would you want to represent your money earned per hour?**
- Function A (slope = 2) would be the most favorable, representing a higher amount of money earned per hour than the other functions.

d. **Which function would give you the highest initial amount of money?**
- Function C (y-intercept = 5) gives the highest initial amount of money (when x = 0, y = 5).

If you have specific functions for A and B, please provide them for more accurate responses.