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.
8 answers