Question

The function y = f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval -3 ≤ x ≤-1?

Answer 1

The average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.

What is the average rate of change?

The average Rate of Change of the function f(x) can be calculated as;

$f(x) = \dfrac{f(b) - f(a)}{b-a}$

Interval -3 ≤ x ≤-1

a = -3, b = -1

f(a) = f(-3) = -20

f(b) = f(-1) = 0

Step 2: Find Average

$f(x) = \dfrac{f(b) - f(a)}{b-a}\\\\\\f(x) = \dfrac{f(-1) - f(-3)}{-1-(-3)}\\\\\\f(x) = \dfrac{0 - (-20)}{2}\\\\f(x) = 10$

Therefore, the average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.

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