To match the descriptions with the correct functions, we first need to analyze the information provided for each function and their characteristics.
Provided Data and Analysis:
Function A and B Marbles Data:
- Function A: The points (0, 1), (4, 9), (8, 17) can be interpreted as a quadratic function.
- Function B: To find the exact representation, we need points, but we might assume a linear progression with a constant slope based on these points.
Function C:
- Function C: \( y = x + 20 \) is a linear function with a y-intercept of 20.
Analyzing Each Function Against Provided Descriptions:
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Function with the greatest rate of change:
- This typically refers to the function with the highest slope.
- Since Function C has a constant slope of 1 (since it’s linear), we compare Function A and B based on how quickly their values increase. Function A appears to be growing faster, especially between (4, 9) to (8, 17).
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Function with the smallest y-intercept:
- Function A's y-intercept is at (0, 1), while Function C has a y-intercept of 20. Without exact values for Function B, we assume its y-intercept is 0.
- Function A has a y-intercept of 1, so Function B (if 0) is the smallest.
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Which function would benefit you the most if it represented your money earned per hour?
- Higher and more favorable rates of change correlate with greater amounts earned. Function A appears favorable with the points given, suggesting it has higher increase values.
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Function with the highest initial amount of money:
- Function C starts with 20 as an initial amount, which is higher than the outputs provided for Function A and Function B.
Final Solution:
Based on the analysis:
- Function with the greatest rate of change: Function A
- Function with the smallest y-intercept: Function B
- Which function would benefit you the most if it represented your money earned per hour?: Function A
- Function with the highest initial amount of money: Function C
Now we can insert these responses into the correct input fields.
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