Match the description with the correct Function. Function A: (0,-2) (1,-2) (8,0). Function B: X Y

Question

0 1
4 9
8 17
Function C: y=x+20
Questions:
Functions 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?
Choose functions A, B or C

Answer 1

To match the descriptions with the correct functions, let's analyze each function one by one.

Function A: (0,-2), (1,-2), (8,0)

• The points indicate that when \(x = 0\), \(y = -2\); when \(x = 1\), \(y = -2\); and when \(x = 8\), \(y = 0\).
• The y-value does not change between \(x = 0\) and \(x = 1\) (indicating a horizontal line segment) and increases as \(x\) increases. Thus, the slope (or rate of change) is not very steep.

Function B:

| X | Y | |---|----| | 0 | 1 | | 4 | 9 | | 8 | 17 |

• To find the rate of change between intervals:
  • From (0, 1) to (4, 9): \((9 - 1)/(4 - 0) = 8/4 = 2\)
  • From (4, 9) to (8, 17): \((17 - 9)/(8 - 4) = 8/4 = 2\)
• The rate of change (slope) is consistent and equals 2 for these intervals.

Function C: \(y = x + 20\)

• This is a linear function with a slope of 1 (indicating a steady rate of change as \(x\) increases), and its y-intercept is \(20\).

Analysis of Questions:

1. Functions with the greatest rate of change?

   • Function B has a rate of change of 2, and Function C has a rate of change of 1. Function A has a very low rate of change.
   • Answer: Function B

2. Function with the smallest y-intercept?

   • Function A has a y-intercept of -2, Function B has a y-intercept of 1, and Function C has a y-intercept of 20.
   • Answer: Function A

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

   • Function B grows steadily, making it beneficial as it indicates increasing money earned (from \(1\) at \(x=0\) to \(17\) at \(x=8\)). Function C also grows but has a lower starting point than Function B, while Function A either stays the same or becomes less beneficial.
   • Answer: Function B

4. Function with the highest initial amount of money?

   • The initial amount can be derived from the y-value at \(x=0\).
   • Function A: -2, Function B: 1, Function C: 20.
   • Answer: Function C

Summary of Answers:

• Greatest rate of change: Function B
• Smallest y-intercept: Function A
• Benefit for money earned per hour: Function B
• Highest initial amount of money: Function C