9. Match the description with the correct Function.

Question

Function A:

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

Answer 1

To correctly match the descriptions with the provided functions, let's analyze each function and the given data points.

Analyzing the Functions:

1. Function A:

   • Data points: (0, 1), (4, 9), (8, 17)
   • To determine the rate of change, let's calculate the slope (rate of change) between the points.
   • From (0, 1) to (4, 9): \[ \text{Slope} = \frac{9 - 1}{4 - 0} = \frac{8}{4} = 2 \]
   • From (4, 9) to (8, 17): \[ \text{Slope} = \frac{17 - 9}{8 - 4} = \frac{8}{4} = 2 \]
   • The rate of change (slope) remains constant at 2.

2. Function B:

   • (Not defined with data points; assumed linear for the sake of comparison)

3. Function C:

   • Equation: \( y = x + 20 \)
   • This function has a slope (rate of change) of 1.

Matching the Descriptions:

1. Function with the greatest rate of change:

   • Function A has a slope of 2, and Function C has a slope of 1. Assuming Function B's rate of change is less than 2, Function A has the greatest rate of change.

2. Function with the smallest y-intercept:

   • For Function A, the y-intercept (when x=0) is 1.
   • For Function C, the y-intercept (when x=0) is 20.
   • Since Function B does not have defined characteristics in the problem, we cannot definitively identify its y-intercept. However, from what's provided, it would be logical to assign Function A as having the smallest defined y-intercept.

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

   • Function A has the highest rate of change (2) compared to Function C (1). Therefore, Function A would benefit you the most since it represents a higher money earned per hour.

4. Function with the highest initial amount of money:

   • Function A starts at 1 (when x=0). Function C starts at 20. Therefore, Function C has the highest initial amount of money.

Final Matches:

• Function with the greatest rate of change: Function A
• Function with the smallest y-intercept: Function A (1 compared to the assumed value for 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 (20)

So, the responses will be:

1. Function A
2. Function A
3. Function A
4. Function C