Question

Function A: Function B: 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?

Function A
Function B
Function C

Answer 1

To analyze the given functions, we need to determine their slopes and y-intercepts. It appears that you provided only **Function A** as \( y = x + 5 \).

However, for context, let's assume the following for Functions B and C as hypothetical linear functions (since their equations are missing):

- **Function A:** \( y = x + 5 \)
- **Function B:** \( y = -2x + 3 \) (hypothetical example with a negative slope)
- **Function C:** \( y = 3x - 1 \) (hypothetical example with a positive slope)

Now we can analyze the functions based on typical understanding of linear functions:

1. **Which function has a negative rate of change (slope)?**
\[ \text{slope of Function A} = 1 \quad (\text{positive}) \]
\[ \text{slope of Function B} = -2 \quad (\text{negative}) \]
\[ \text{slope of Function C} = 3 \quad (\text{positive}) \]
**Answer:** Function B has a negative rate of change.

2. **Which function has the smallest y-intercept?**
The y-intercept is the constant term in each of the function equations.
- Function A: \( y \)-intercept = 5
- Function B: \( y \)-intercept = 3
- Function C: \( y \)-intercept = -1
**Answer:** Function C has the smallest y-intercept.

3. **Which function would you want to represent your money earned per hour?**
Generally, you would prefer a function with a positive slope that represents increased earnings over time.
- Function A: \( y = x + 5 \) (1 dollar increase per hour)
- Function B: \( y = -2x + 3 \) (decreases with time)
- Function C: \( y = 3x - 1 \) (3 dollars increase per hour)
**Answer:** Function C would be desirable to represent money earned per hour, as it has the highest rate of increase.

4. **Which function would give you the highest initial amount of money?**
The initial amount corresponds to the y-intercept:
- Function A: \( y \)-intercept = 5
- Function B: \( y \)-intercept = 3
- Function C: \( y \)-intercept = -1
**Answer:** Function A gives the highest initial amount of money.

In summary:
- Negative rate of change: **Function B**
- Smallest y-intercept: **Function C**
- Represents money earned per hour: **Function C**
- Highest initial amount: **Function A**

If you have specific equations for Functions B and C, I can provide more accurate answers.