Question

Match each Interval with its corresponding average rate of change for f(x) = (x + 3)^2.

-6 ≤ x ≤ -4
-3 ≤ x ≤ -2
-3 ≤ x ≤ 0
-4 ≤ x ≤ -3
-3 ≤ x ≤ 1
-[infinity] ≤ x ≤ -4
a) -6
b) -3
c) 6
d) -4

Answer 1

The average rate of change for f(x) = (x + 3)² is calculated for different intervals.

Step-by-step explanation:

The average rate of change of a function is calculated by finding the change in the function's value over a given interval and dividing it by the change in the independent variable.

For the function f(x) = (x + 3)², the average rate of change can be calculated for each interval:

• Interval -6 ≤ x ≤ -4: The average rate of change is 6.
• Interval -3 ≤ x ≤ -2: The average rate of change is 5.
• Interval -3 ≤ x ≤ 0: The average rate of change is 3.
• Interval -4 ≤ x ≤ -3: The average rate of change is 2.
• Interval -3 ≤ x ≤ 1: The average rate of change is 6.
• Interval -∞ ≤ x ≤ -4: The average rate of change is 0.