Compare the following functions:
Function A: y=4x −5
Function B:
x y
0 0
1 1
2 4
3 9
What is the slope/rate of change of Function A?
What is the slope/rate of change of Function B between f(0) and f(1)?
What is the slope/rate of change of Function B between f(1) and f(2)?
What is the slope/rate of change of Function B between f(2) and f(3)?
The slope of Function A is
. The slope of Function B is
The slope/rate of change of Function A is 4.
To find the slope/rate of change of Function B between f(0) and f(1), we can use the formula for slope:
slope = (change in y) / (change in x)
Between f(0) and f(1), the change in x is 1-0 = 1, and the change in y is 1-0 = 1. Therefore, the slope/rate of change is 1/1 = 1.
Between f(1) and f(2), the change in x is 2-1 = 1, and the change in y is 4-1 = 3. Therefore, the slope/rate of change is 3/1 = 3.
Between f(2) and f(3), the change in x is 3-2 = 1, and the change in y is 9-4 = 5. Therefore, the slope/rate of change is 5/1 = 5.
The slope of Function A is 4. The slope of Function B is 1 between f(0) and f(1), 3 between f(1) and f(2), and 5 between f(2) and f(3).