Question

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

Answer 1

I believe the proper form of this question is actually... as I have also come across this question.

"For the graphed function f(x) = (2)^(x + 2) + 1, calculate the average rate of change from x = −1 to x = 0."

Explanation:

the y2 - y1/ x2 - x1, will actually be (-1,3) and (0,5).

This means you will get a 5 + 1 (because subtracting a -1 is the same as adding 1) over 0 - 3.

Next you have 6/-3 which will give you a answer of -2

Now I do believe the proper answer is actually 2 because the graph shows a chart that is growth, not decay, but the math gives a -2 which is confusing.

Answer 2

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

Answer: 2