Question

Use the graph below for this question:

graph of parabola going through negative 1, 7 and negative 3, 9.

What is the average rate of change from x = −1 to x = −3?

5
−3
1
−1

Answer 1

What they want here is the slope of the line through (1,7) and (-3,9)

Using the slope formula, we get...

m = (y2-y1)/(x2-x1)
m = (9-7)/(-3-(-1))
m = (9-7)/(-3+1)
m = 2/(-2)
m = -1

So the answer must be choice D) -1

If you draw a line through these two points, the line will slope downward (move from left to right). Each time you go down 1, you go to the right 1.

Answer 2

The correct option is 4. The average rate of change from x = −1 to x = −3 is -1.

Explanation:

It is given that the graph of parabola going through (-1,7) and (-3,9).

It means the value of at x=-1 is 7.

`f(-1)=7`

The value of at x=-3 is 9.

`f(-3)=9`

The slope of a function f(x) for the interval [a,b] is

`m=(f(b)-f(a))/(b-a)`

We have to find the average rate of change from x = −1 to x = −3. Here a=-1 and b=-3. So the average rate of change from x = −1 to x = −3 is

`m=(f(-3)-f(-1))/(-3-(-1))`

`m=(9-7)/(-3+1)`

`m=(2)/(-2)`

`m=-1`

The average rate of change from x = −1 to x = −3 is -1. Therefore the correct option is 4.