Match the description with the correct Function.

Question

(8, 0)
-5
10
Function A:
(4, - 1)
(0, -2)
Function B:
0
4
1
9
17
Function C: y = x + 20
(4 points)
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
:: Function A
:: Function B
:: Function C

Answer 1

To match the descriptions with the correct functions, we need to analyze each function based on the provided points and equations.

Functions:

1. Function A:

   • Points: (8, 0), (4, -1), (0, -2)
   • To find the rate of change, we can use the points:
     • From (0, -2) to (8, 0): \[ \text{Rate of change} = \frac{0 - (-2)}{8 - 0} = \frac{2}{8} = \frac{1}{4} \]

2. Function B:

   • Points: (0, 0), (1, 4), (9, 10), (17, ?)
   • Since we only have starting points (initial amount) and sample calculations could be done from the line segments available.
   • It's implied that function B starts at (0, 0) which is a y-intercept of 0.

3. Function C:

   • Equation: \(y = x + 20\)
   • The y-intercept is 20 (when \(x = 0\)).

Analyzing the functions based on descriptions:

1. Function with the greatest rate of change:

   • We need to compare the rates of change. We only calculated the rate for Function A and didn't calculate the exact rates for B and C's line segments specifically, but since Function C has a constant change of 1 (from y = x + 20) and B could have variable changes, we can say for sure C has a constant rate of change.
   • Here it seems like Function C probably has the most consistent increase.

2. Function with the smallest y-intercept:

   • Function A: y-intercept is -2.
   • Function B: y-intercept is 0.
   • Function C: y-intercept is 20.
   • Therefore, 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 gives negative earnings in certain ranges.
   • Function B has a y-intercept of 0, suggesting you would earn some money only after spending some hours (initial earning).
   • Function C has the highest y-intercept at 20, strongly suggesting a favorable rate of earnings.

4. Function with the highest initial amount of money:

   • Function C: y-intercept = 20 (highest).
   • Function B: 0 (starting).
   • Function A: -2 (negative starting).

Final Matching:

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

So the most suitable matches are:

1. Greatest rate of change: Function C
2. Smallest y-intercept: Function A
3. Benefit most if representing money: Function C
4. Highest initial amount: Function C

Final answers are:

• Function with the greatest rate of change: Function C
• Function with the smallest y-intercept: Function A
• Benefit the most: Function C
• Highest initial amount: Function C