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Match the description with the correct Function.Function A: Function B: x y 0149817 Function C: y=x+20 (4 points)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.Function with the greatest rate of change Function with the smallest y-intercept Which function would benefit you the most if it represented your money earned per hour?Function with the highest initial amount of money

1 answer

To match the descriptions with the correct functions, let's analyze the functions you've provided.

  1. Function A:

    • From the data you've given, it seems to be an unspecified function.

  2. Function B:

    • The table seems to have values representing pairs \( (x, y) \):
    • (0, 14), (9, 8), (17, ??) (missing value) -- assuming point values could be calculated or extrapolated.

  3. Function C:

    • Given as \( y = x + 20 \), which is a linear function with a slope of 1 and a y-intercept of 20.

Analyzing Functions

  • Function with the greatest rate of change:

    • The rate of change can be assessed by looking at the slopes. If Function C has the highest slope (which is 1), we'll need to see whether Function A or Function B has a steeper slope (if enough data is provided).

  • Function with the smallest y-intercept:

    • Here, you can directly evaluate the y-intercepts:
    • Function C has a y-intercept of 20.
    • For Function B, if (0, 14) is its only given point, its y-intercept is 14. Hence, it is the smallest so far.

  • Which function would benefit you the most if it represented your money earned per hour:

    • This would be the function with the highest slope (or rate of change), as it represents how your earnings increase per unit of time.

  • Function with the highest initial amount of money:

    • This would simply be the value of y at \( x = 0 \) or the y-intercept (or any given data point for Function A) where it shows how much you start with.

Matching Responses

With that analysis in mind, we can infer the following matches:

Function with the greatest rate of change:

  • Need data to confirm but likely Function A or Function C depending on their slopes.

Function with the smallest y-intercept:

  • Function B (y-intercept of 14).

Which function would benefit you the most if it represented your money earned per hour:

  • Function C since it has a positive slope.

Function with the highest initial amount of money:

  • Assuming Function B has \( y=14 \) at \( x=0\), it could be the answer unless Function A has a higher specified initial amount.

Recommendations for Input Structure

  1. Greatest rate of change: Function C (tentatively, assuming further data for other functions).
  2. Smallest y-intercept: Function B.
  3. Benefit most (money per hour): Function C.
  4. Highest initial amount: Function B (until more data on Function A is available).

If any values or specific information are available for Function A, that could impact the conclusions drawn here.