Answered

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

Verified Answer :

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:

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

Step-by-step 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

\(m=\frac{f(b)-f(a)}{b-a}\)

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

\(m=\frac{f(-3)-f(-1)}{-3-(-1)}\)

\(m=\frac{9-7}{-3+1}\)

\(m=\frac{2}{-2}\)

\(m=-1\)

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

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