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:
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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. -
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.
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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.
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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.
1 answer