Let's analyze each function based on the provided information.
a. Which function has the greatest rate of change (slope)?
Function A: We can determine the slope by using the points it provides. Between Dot 1 (-4, 0) and Dot 4 (2, 3):
- Slope = (Y2 - Y1) / (X2 - X1) = (3 - 0) / (2 - (-4)) = 3 / 6 = 0.5
Function B: The slope can be calculated between the points given. Between the first two points (0, 3) and (4, -9):
- Slope = (-9 - 3) / (4 - 0) = -12 / 4 = -3
Function C: This equation is linear (y = x + 5). The slope (rate of change) is 1.
- Slope of Function A: 0.5
- Slope of Function B: -3
- Slope of Function C: 1
Greatest slope: Function C has the greatest rate of change (1).
b. Which function has the smallest y-intercept?
- Function A: The y-intercept is the value at x=0, which is 2 (Dot 3).
- Function B: The y-intercept can be calculated, but since it is a set of points, we consider the point (0, 3) which gives a y-intercept of 3.
- Function C: The y-intercept is 5 (because y = x + 5).
Smallest y-intercept: Function A has the smallest y-intercept (2).
c. Which function would you want to represent your money earned per hour?
You would typically want a function with a positive slope which represents gaining money over time.
- Function A (positive slope of 0.5)
- Function C (positive slope of 1)
- Function B has a negative slope (-3) which would not be appropriate for representing money earned.
Best representation for money earned: Function C is preferred as it has a higher slope of 1, meaning you earn $1 per hour compared to $0.50 per hour in Function A.
d. Which function would give you the highest initial amount of money?
The initial amount of money corresponds to the y-intercept of the function.
- Function A: 2
- Function B: 3
- Function C: 5
Highest initial amount of money: Function C gives the highest initial amount of money ($5).
Summary of Answers:
a. Function C has the greatest rate of change (slope).
b. Function A has the smallest y-intercept.
c. Function C would represent money earned per hour.
d. Function C would give the highest initial amount of money.
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