To analyze the functions provided, let's break each question down step by step:
Function A
Points: (-4, 0), (-2, 1), (0, 2), (2, 3)
To find the slope (rate of change):
Using two points, for example, (0, 2) and (2, 3):
You can calculate the slope between any two points to find this was consistent; the slope is .
Function B
Table:
Finding the slope between the first two points (0, 3) and (4, -9):
Finding the slope between the second two points (4, -9) and (8, -21):
The slope is consistently .
Function C
Equation:
The slope (rate of change) is:
1 (the coefficient of x).
Comparing Slopes
- Function A: slope =
- Function B: slope =
- Function C: slope =
Greatest Rate of Change:
- Function C has the greatest slope of .
Finding y-intercepts
- Function A's y-intercept: When , .
- Function B's y-intercept: When , .
- Function C's y-intercept: When , .
Smallest Y-Intercept:
- Function A:
- Function B:
- Function C:
The smallest y-intercept is from Function A.
Money Earned per Hour
Generally, you might prefer a function with a positive slope representing earnings, and you want it to be as high as possible.
- Function A has a positive slope ().
- Function C has a slope of .
Function C would represent the best option for money earned per hour since it has a positive slope and does not dip.
Highest Initial Amount of Money
The initial amount of money is represented by the y-intercept.
- Function A =
- Function B =
- Function C =
The highest initial amount of money is from Function C.
Answers
a. Function C (greatest rate of change)
b. Function A (smallest y-intercept)
c. Function C (best for money earned per hour)
d. Function C (highest initial amount of money)
Would you like to clarify further or provide more detail for any of these points?