Ask a New Question
Menu

function A:

(0,-2), (4,-1), and (8,0)

function B:
(1, 0), (4, 9), and (8, 17)

function C:
y = x + 20

1. function with the greatest rate of change _____

2. function with the smallest y-intercept _______

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

Function with the highest amount of inital money

1 answer

Let's analyze the functions based on the information provided:

Given Functions:

  1. Function A: Points (0, -2), (4, -1), and (8, 0)

    • Slope calculation (rate of change between points):
      • Between (0, -2) and (4, -1): \[ \text{slope} = \frac{-1 - (-2)}{4 - 0} = \frac{1}{4} \]
      • Between (4, -1) and (8, 0): \[ \text{slope} = \frac{0 - (-1)}{8 - 4} = \frac{1}{4} \]
    • Rate of change: Constant slope of \( \frac{1}{4} \).

  2. Function B: Points (1, 0), (4, 9), and (8, 17)

    • Slope calculation:
      • Between (1, 0) and (4, 9): \[ \text{slope} = \frac{9 - 0}{4 - 1} = \frac{9}{3} = 3 \]
      • Between (4, 9) and (8, 17): \[ \text{slope} = \frac{17 - 9}{8 - 4} = \frac{8}{4} = 2 \]
    • Rate of change: Variable, but maximum rate is \( 3 \).

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

    • This is a linear function with a constant slope of \( 1 \).

Answers:

  1. Function with the greatest rate of change:

    • Function B (maximum slope of \( 3 \)).

  2. Function with the smallest y-intercept:

    • From Function A, the y-intercept is \( -2 \).
    • From Function B, substituting \( x = 0 \) (or looking at (1,0)): \( y = 0 \).
    • For Function C, the 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:

    • The best option would be the function with a consistently positive increase over time, which is Function B as it has the highest rate of change (slope) of \( 3 \), indicating higher earnings as x increases.

  4. Function with the highest initial money:

    • Function A starts at \( -2 \) (at x = 0).
    • Function B starts at \( 0 \) (at x = 1).
    • Function C starts at \( 20 \) (when x = 0).
    • Hence, Function C has the highest initial money at \( 20 \).

Summary of Answers:

  1. Function with the greatest rate of change: Function B
  2. Function with the smallest y-intercept: Function A
  3. Function that would benefit the most in money earned per hour: Function B
  4. Function with the highest amount of initial money: Function C