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Function B:

x y
0 1
4 9
8 17


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 analyze the functions B and C, we need to look at their rates of change, y-intercepts, initial amounts, and applicability in terms of earnings.

  1. Function with the greatest rate of change:

    • Function B: The changes in y-values relative to x-values are as follows:
      • From (0, 1) to (4, 9): Change in y = \(9 - 1 = 8\); Change in x = \(4 - 0 = 4\) → Rate of change = \(8/4 = 2\)
      • From (4, 9) to (8, 17): Change in y = \(17 - 9 = 8\); Change in x = \(8 - 4 = 4\) → Rate of change = \(8/4 = 2\)

    The average rate of change of Function B = 2.

    • Function C: This function is linear and has a constant slope of 1.

    Therefore, Function B has the greatest rate of change.

  2. Function with the smallest y-intercept:

    • Function B: The y-intercept occurs at \(x=0\), which is \(y = 1\).
    • Function C: At \(x=0\), \(y = 0 + 20 = 20\).

    Therefore, Function B has the smallest y-intercept.

  3. Which function would benefit you the most if it represented your money earned per hour?

    • Function B shows a higher rate of change (2) versus Function C (1). So, Function B would benefit you more as it represents a higher earning as hours increase.

  4. Function with the highest initial amount of money:

    • Function B: The initial amount (y-value when \(x=0\)) is \(y = 1\).
    • Function C: The initial amount is \(y = 20\).

    Therefore, Function C has the highest initial amount.

Now, placing the appropriate responses:

  • Function with the greatest rate of change: Function B
  • Function with the smallest y-intercept: Function B
  • Which function would benefit you the most if it represented your money earned per hour?: Function B
  • Function with the highest initial amount of money: Function C