Question

The function y, equals, f, of, xy=f(x) is graphed below. What is the average rate of change of the function f, of, xf(x) on the interval minus, 3, is less than or equal to, x, is less than or equal to, 8−3≤x≤8?
x

the numbers for 3 and 8 were -90 and 20 so 3/-90 and 8/20

Answer 1

To find the average rate of change of the function \( f(x) \) on the interval \([-3, 8]\), we use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a = -3 \) and \( b = 8 \).

From the information given:

- \( f(-3) = -90 \)
- \( f(8) = 20 \)

Substituting these values into the formula:

\[
\text{Average Rate of Change} = \frac{f(8) - f(-3)}{8 - (-3)} = \frac{20 - (-90)}{8 + 3} = \frac{20 + 90}{11} = \frac{110}{11} = 10
\]

Thus, the average rate of change of the function \( f(x) \) on the interval \([-3, 8]\) is \( 10 \).