Question

Question
Function A:
Graph points: (-4,0) , (-2,1) , (0,2) , (2,3)

Function B:

x y
0 3
4 -9
8 -21
Function C: y=x+5

(4 points)

Which function has a negative rate of change (slope)?

Which function has the smallest y-intercept?

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

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

Answer 1

To determine the answers to the questions, we will analyze each function based on the given information.

**Function A**: The points given are (-4,0), (-2,1), (0,2), (2,3).
We can calculate the slope (rate of change) between the points:
1. From (-4,0) to (-2,1):
\[
\text{Slope} = \frac{1 - 0}{-2 - (-4)} = \frac{1}{2}
\]
2. From (-2,1) to (0,2):
\[
\text{Slope} = \frac{2 - 1}{0 - (-2)} = \frac{1}{2}
\]
3. From (0,2) to (2,3):
\[
\text{Slope} = \frac{3 - 2}{2 - 0} = \frac{1}{2}
\]

The rate of change (slope) for Function A is positive (1/2).

**Function B**: Given points are (0,3), (4,-9), (8,-21). Calculate the slope between the points:
1. From (0,3) to (4,-9):
\[
\text{Slope} = \frac{-9 - 3}{4 - 0} = \frac{-12}{4} = -3
\]
2. From (4,-9) to (8,-21):
\[
\text{Slope} = \frac{-21 - (-9)}{8 - 4} = \frac{-12}{4} = -3
\]

The rate of change (slope) for Function B is negative (-3).

**Function C**: The equation is \( y = x + 5 \). Here, the slope is 1 (positive).

### Answers to the Questions:

1. **Which function has a negative rate of change (slope)?**
- **Function B** has a negative rate of change.

2. **Which function has the smallest y-intercept?**
- For Function A, the y-intercept is 2 (when x=0).
- For Function B, the y-intercept is 3 (when x=0).
- For Function C, the y-intercept is 5 (when x=0).
- **Function A** has the smallest y-intercept (2).

3. **Which function would you want to represent your money earned per hour?**
- A function with a positive slope (rate of change) is preferable for representing income.
- **Function A** or **Function C** could represent money earned per hour, but since Function A has a stronger upward trend (from 0 to 3), it might be more representative than C, which grows linearly. Thus, **Function A** is the better choice.

4. **Which function would give you the highest initial amount of money?**
- Looking at the y-intercepts again:
- Function A gives 2 at x=0.
- Function B gives 3 at x=0.
- Function C gives 5 at x=0.
- **Function C** gives the highest initial amount of money (5).

In summary:
1. Function B
2. Function A
3. Function A
4. Function C