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 match the descriptions with the correct Function, we first need to analyze Functions A, B, and C based on the information provided.

Function A has the following data points:

• (0, 1): When x = 0, y = 1
• (4, 9): When x = 4, y = 9
• (8, 17): When x = 8, y = 17

We can calculate the rate of change (slope) between the points:

1. Between (0, 1) and (4, 9): \[ \text{slope} = \frac{9 - 1}{4 - 0} = \frac{8}{4} = 2 \]

2. Between (4, 9) and (8, 17): \[ \text{slope} = \frac{17 - 9}{8 - 4} = \frac{8}{4} = 2 \]

The rate of change is constant at 2.

Function B can be inferred from the table but is not directly given. However, it appears to show values, but without further information on outputs like a formula, we can't establish a rate of change or intercept.

Function C is given as \( y = x + 20 \).

• The initial value (y-intercept) is 20 when \( x = 0 \).

Now, let's evaluate each function based on the descriptions provided:

1. Function with the greatest rate of change:

   • Since we determined that the rate of change for Function A is 2, we do not have enough information about Function B, but if it has a different slope, it may be prioritized here. Without specific values for Function B, we might consider Function A for now.

2. Function with the smallest y-intercept:

   • Function A starts at y = 1.
   • Function C has a y-intercept of 20.
   • Hence, Function A has the smallest y-intercept.

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

   • Function A appears to be linear with a steady growth over time versus Function C with a higher y-intercept but lower slope (the later doesn't show a drastic percentage rate difference). Therefore, based on hourly growth, Function A might be preferable.

4. Function with the highest initial amount of money:

   • Function C starts at 20, which is the highest initial y-value based on the y-intercept.

Based on this analysis, we can match the responses:

• Function with the greatest rate of change: (function to be determined based on further data for B)
• Function with the smallest y-intercept: Function A
• 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

Final matching:

1. Function with the greatest rate of change: Function A (tentatively, but we need more data about Function B)
2. Function with the smallest y-intercept: Function A
3. Which function would benefit you the most if it represented your money earned per hour: Function A
4. Function with the highest initial amount of money: Function C

(Note: For more accurate matching, specific details about Function B are needed.)