Question

For the graphed function f(x) = −(5)x − 3 + 2, calculate the average rate of change from x = 3 to x = 4.

Answer 1

just find the slope between the 2 points
slope between (3,1) and (4,-3) is (-3-1)/(4-3)=-4/1=-4

answer is first option

Answer 2

-4 is the average rate of change from 3 to 4

Explanation:

Given that

`f(x) =( -5)^(x-3) +2`

Average rate of change is defined as the fraction of change in f(x) value to change in x value.

Here we have x values as 3 and 4.

To find the average rate of change from x=3 to x=4

Average rate of change = change in f(x)/change in x

Change in x = 4-3 =1

`f(4) = -5^(4-3) +2 = -3\\f(3) = 1\\f(4)-f(3) = -3-1 =-4`

Average rate of change = -4/1 = -4