Question

there a three functions
Function A shows a graph with a positive slope and 4 dots, Dot 1 is (-4, 0), Dot 2 is (-2, 1), Dot 3 is (0, 2), and Dot 4 is (2, 3)
Function B is a a graph:
X: 0, 4, 8
Y: 3, -9, -21
and function C is y = x + 5
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

Let's analyze each function based on the provided information.

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

**Function A**: We can determine the slope by using the points it provides. Between Dot 1 (-4, 0) and Dot 4 (2, 3):
- Slope = (Y2 - Y1) / (X2 - X1) = (3 - 0) / (2 - (-4)) = 3 / 6 = 0.5

**Function B**: The slope can be calculated between the points given. Between the first two points (0, 3) and (4, -9):
- Slope = (-9 - 3) / (4 - 0) = -12 / 4 = -3

**Function C**: This equation is linear (y = x + 5). The slope (rate of change) is 1.

- Slope of Function A: 0.5
- Slope of Function B: -3
- Slope of Function C: 1

**Greatest slope**: Function C has the greatest rate of change (1).

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

- **Function A**: The y-intercept is the value at x=0, which is 2 (Dot 3).
- **Function B**: The y-intercept can be calculated, but since it is a set of points, we consider the point (0, 3) which gives a y-intercept of 3.
- **Function C**: The y-intercept is 5 (because y = x + 5).

**Smallest y-intercept**: Function A has the smallest y-intercept (2).

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

You would typically want a function with a positive slope which represents gaining money over time.

- **Function A** (positive slope of 0.5)
- **Function C** (positive slope of 1)
- **Function B** has a negative slope (-3) which would not be appropriate for representing money earned.

**Best representation for money earned**: Function C is preferred as it has a higher slope of 1, meaning you earn $1 per hour compared to $0.50 per hour in Function A.

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

The initial amount of money corresponds to the y-intercept of the function.

- **Function A**: 2
- **Function B**: 3
- **Function C**: 5

**Highest initial amount of money**: Function C gives the highest initial amount of money ($5).

### Summary of Answers:
a. Function C has the greatest rate of change (slope).
b. Function A has the smallest y-intercept.
c. Function C would represent money earned per hour.
d. Function C would give the highest initial amount of money.