Question

Given the function, fx) = x2-3, calculate the average rate of change of the function from x = 1 to x = 3.

-2
4
8
-12

Answer 1

The average rate of change is 4.

Explanation:

We are given the function:

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

And we want to find the average rate of change from x = 1 to x = 3.

The average rate of change is synonymous with the slope. So, we can evaluae the endpoints and find the slope between them.

The first endpoint is:

`f(1)=(1)^2-3=-2`

The second endpoint is:

`f(3)=(3)^2-3=6`

This yields the two poins (1, -2) and (3, 6). The slope between them will be:

`\displaystyle ARC=(6-(-2))/(3-1)=(8)/(2)=4`

Hence, the average rate of change is 4.