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:

$\frac{\Delta f(x)}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

In this case, we have:

$\frac{\Delta f(x)}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{f(0)-f(-1)}{0-(-1)}=\frac{5-2}{0+1}=3$

The average rate of change is 3 in this interval.