Question

Find the average rate of change over the interval [-1,2] (from x = -1 to x = 2) for the graph below

What is the coordinate where x=-1 ?

What is the coordinate where x=2?

What is the rate of change between those two points?

Answer 1

Hello!

Find the coordinate where x = -1:

At x = -1, y = 1, so the coordinate is (-1, 1).

Find the coordinate where x = 2:

At x = 2, y = -2, so the coordinate is (2, -2).

Find the rate of change between the points using the slope formula:

`slope = (y_(2)-y_(1))/(x_(2)-x_(1))`

Plug in the coordinates above:

`slope = (-2-1)/(2-(-1))`

Simplify:

`slope = (-3)/(3) = -1`

Thus, the rate of change between the points is -1.