Question

What is the average rate of change of f(x) = -2x + 1 from x = -5 to x = 1?

a) -3
b) -2
c) -1
d) 0

Answer 1

b) -2

The average rate of change of f(x) = -2x + 1 from x = -5 to x = 1 is -2.

Step-by-step explanation:

To find the average rate of change of the function f(x) = -2x + 1 from x = -5 to x = 1, we need to calculate the difference in the function values at the two endpoints and then divide by the difference in the x-coordinates. The difference in function values is f(1) - f(-5), which is (-2(1) + 1) - (-2(-5) + 1) = -1 - 11 = -12. The difference in x-coordinates is 1 - (-5) = 6. So the average rate of change is -12/6 = -2. Therefore, the correct answer is b) -2.