For the graphed function f(x) = (2)x + 2 + 1, calculate the average rate of change from x = −1 to x = 0. graph of f of x equals 2 to the x plus 2 power, plus 1. (6 points) −2 2 3 −3

Next time you should write the correct form of equation because it affects greatly the answer. I believe the correct form would be:

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

where the second 2 is a power of x

The average rate of change is also defined as the slope of the equation. Therefore:

average rate of change = slope

Where slope is:

m = (y2 – y1) / (x2 – x1) = [f (0) – f (-1)] / (x2 – x1)

Calculating for f (0): x2 = 0

f (0) = 2 * 0^2 + 1 = 1

Calculating for f (-1): x1 = -1

f (-1) = 2 * (-1)^2 + 1 = 3

Substituting the known values to the slope equation:

average rate of change = (1 – 3) / (0 – 1)

average rate of change = -2 / -1

average rate of change = 2

2