Compare the following functions:
Function A: y=4x −5
�
=
4
�
−
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.
The slope/rate of change of Function B between f(0) and f(1) is 1.
The slope/rate of change of Function B between f(1) and f(2) is 3.
The slope/rate of change of Function B between f(2) and f(3) is 5.
The slope of Function A is 4. The slope of Function B is not constant and varies between different intervals.
To find the slope/rate of change of a function, we need to determine the difference in the y-values (vertical change) divided by the difference in the x-values (horizontal change) between two points on the function.
For Function A:
The equation is y = 4x - 5. Since this is a linear function in the form y = mx + c (where m is the slope), we can directly identify the slope from the equation. In this case, the slope of Function A is 4.
For Function B:
Given the table of values, we can calculate the slope/rate of change between different points.
Between f(0) and f(1):
To find the slope between these two points, we need to calculate the difference in y-values divided by the difference in x-values.
(1 - 0) / (1 - 0) = 1 / 1 = 1
Therefore, the slope/rate of change between f(0) and f(1) for Function B is 1.
Between f(1) and f(2):
Again, we calculate the difference in y-values divided by the difference in x-values.
(4 - 1) / (2 - 1) = 3 / 1 = 3
So, the slope/rate of change between f(1) and f(2) for Function B is 3.
Between f(2) and f(3):
Calculating the slope in the same way,
(9 - 4) / (3 - 2) = 5 / 1 = 5
The slope/rate of change between f(2) and f(3) for Function B is 5.
Therefore, the slope of Function A is 4, and the slopes of Function B between f(0) and f(1), f(1) and f(2), and f(2) and f(3) are 1, 3, and 5 respectively.
The slope, or rate of change, of a linear function is given by the coefficient of x in the equation.
For Function A: y = 4x - 5, the slope is 4.
For Function B, we can determine the slope between each pair of points.
Slope between f(0) and f(1):
Slope = Change in y / Change in x
= (1 - 0) / (1 - 0)
= 1 / 1
= 1
Slope between f(1) and f(2):
Slope = Change in y / Change in x
= (4 - 1) / (2 - 1)
= 3 / 1
= 3
Slope between f(2) and f(3):
Slope = Change in y / Change in x
= (9 - 4) / (3 - 2)
= 5 / 1
= 5
Therefore, the slope of Function A is 4. The slope of Function B between f(0) and f(1) is 1, between f(1) and f(2) is 3, and between f(2) and f(3) is 5.