Question

For the graphed function f(x) = (2)X + 2 + 1, calculate the average rate of change from x=-1 to x=0. 5 5 -3 2 2 -2 2 03 0-3

Answer 1

We have a function f(x):

`f(x)=2^((x+2))+1`

We have to calculate the average rate change for x=-1 to x=0.

We can express an average rate of change as:

`(\Delta f(x))/(\Delta x)=(f(x_2)-f(x_1))/(x_2-x_1)`

In this case, we have:

`(\Delta f(x))/(\Delta x)=(f(x_2)-f(x_1))/(x_2-x_1)=(f(0)-f(-1))/(0-(-1))=(5-2)/(0+1)=3`

The average rate of change is 3 in this interval.