Average Rate of Change Practice

Question

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Question
Use the formula f(b)−f(a)b−a
to calculate the average rate of change over the interval [−2,0]
given the function table for f(x)=x2+6x+8
. Express your answer as an integer.

x f(x)
−3
−1
−2
0
−1
3
0 8
(1 point)
The average rate of change is
.

Answer 1

To find the average rate of change of the function \( f(x) = x^2 + 6x + 8 \) over the interval \([-2, 0]\), we will use the formula for average rate of change:

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

where \( a = -2 \) and \( b = 0 \).

First, we need to calculate \( f(-2) \) and \( f(0) \):

1. Calculate \( f(-2) \): \[ f(-2) = (-2)^2 + 6(-2) + 8 = 4 - 12 + 8 = 0 \]

2. Calculate \( f(0) \): \[ f(0) = (0)^2 + 6(0) + 8 = 0 + 0 + 8 = 8 \]

Now that we have both function values, we can plug these into the average rate of change formula:

\[ \text{Average Rate of Change} = \frac{f(0) - f(-2)}{0 - (-2)} = \frac{8 - 0}{0 + 2} = \frac{8}{2} = 4 \]

Thus, the average rate of change over the interval \([-2, 0]\) is \(\boxed{4}\).