To match the descriptions with the correct functions, let's clarify what each description implies:
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Function with the greatest rate of change: This refers to a function that increases (or decreases) the fastest. In a linear equation \( y = mx + b \), the rate of change is represented by the slope \( m \). Thus, a function with the greatest rate of change would have the largest slope.
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Function with a smaller Y intercept: The Y-intercept is the point where the function crosses the Y-axis, represented by \( b \) in the linear equation. A function with a smaller Y-intercept would have a lower starting point on the Y-axis.
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Function that would benefit you the most if it represented your money earned per hour: This indicates a positive function with a significant slope that represents earnings. The higher the earnings per hour (evaluation of rate), the better it would be for you.
Matching:
- Function with the greatest rate of change: The function with the largest slope.
- Function with a smaller Y intercept: The function with the lowest value of \( b \).
- Function that would benefit you the most if it represented your money earned per hour: The function with the highest positive rate of change (slope), indicating the most money earned per hour.
In summary:
- Greatest rate of change → Function with the largest slope
- Smaller Y intercept → Function with the lowest \( b \)
- Benefit for money earned → Function with the highest slope (indicating higher earnings per hour)
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