Question

What is the average rate of change in f(x) on the interval [5,9]?

A)-1.5
B)6/4
C)4
D)-6

Answer 1

A) -1.5

Explanation:

We can find the average rate of change of a function over an interval using the formula:

(f(x2) - f(x1)) / (x2 - x1), where

• (x2, f(x2)) is the rightmost part of the interval.
• In this problem, 9 is our x2 and f(x2) is 3 since 3 is the y-coordinate when you plug in 9 for f(x))
• (x1, f(x1)) is the leftmost part of the interval of the interval.
• In this case, 5 is our x1 and f(x1) is 9 since 9 is the y-coordinate when you plug in 5 for f(x).

Thus, we can plug in (9, 3) for (x2, f(x2)) and (5, 9) for (x1, f(x1)) to find the average rate of change in f(x) on the interval [5,9].

(3 - 9) / (9 - 5)

(-6) / (4)

-3/2

is -3/2.

If we convert -3/2 into a normal number, we get -1.5

Thus, the average rate of change in f(x) on the interval [5,9] is -1.5

Answer 2

Explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

`\boxed{\textsf{Average rate of change}=(f(b)-f(a))/(b-a)}`

In this case, we need to find the average rate of change on the interval [5, 9], so a = 5 and b = 9.

From inspection of the given graph:

• f(5) = 9
• f(9) = 3

Substitute the values into the formula:

`\textsf{Average rate of change}=(f(9)-f(5))/(9-5)=(3-9)/(9-5)=(-6)/(4)=-1.5`

Therefore, the average rate of change of f(x) over the interval [5, 9] is -1.5.