Find the average rate of change for the function between the give values.
f(x)=-4x + 8; from 1 to 2
A. evaluate the function at x = 2
B. evaluate the function at x = 1
then
Subtract B from A
divide by the change in x from 1 to 1 which is 2-1 = 1
So the answer is simply
(A-B)
The book has the correct answer at -4..how'd they arrive at that?
A -4(2)+ 8 = 0
B -4(1)+ 8 = 4
A-B = 0 - 4 = -4
To find the average rate of change for the function between the given values, we need to calculate the difference in the function's values and divide it by the difference in the input values.
Step 1: Determine the function values at the given input values.
Plug in x = 1 into the function f(x) = -4x + 8:
f(1) = -4(1) + 8 = -4 + 8 = 4
Plug in x = 2 into the function f(x) = -4x + 8:
f(2) = -4(2) + 8 = -8 + 8 = 0
Step 2: Calculate the difference in the function values.
Difference in function values = f(2) - f(1) = 0 - 4 = -4
Step 3: Calculate the difference in the input values.
Difference in input values = 2 - 1 = 1
Step 4: Divide the difference in function values by the difference in input values to find the average rate of change.
Average rate of change = (Difference in function values) / (Difference in input values) = -4 / 1 = -4
Therefore, the average rate of change for the function f(x) = -4x + 8 from 1 to 2 is -4.