Question

Find the average rate of change over the interval [-2,0] for the function f(x)=x2+4x+3f(x)=x2+4x+3 .(1 point) Responses −12−12negative 1 half 12121 half -2 -2 2

Answer 1

To find the average rate of change of the function \( f(x) = x^2 + 4x + 3 \) over the interval \([-2, 0]\), we can use the formula for the 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 find the values of \( f(-2) \) and \( f(0) \).

1. Calculate \( f(-2) \):
\[
f(-2) = (-2)^2 + 4(-2) + 3 = 4 - 8 + 3 = -1
\]

2. Calculate \( f(0) \):
\[
f(0) = 0^2 + 4(0) + 3 = 3
\]

Now, we can plug these values into the average rate of change formula:

\[
\text{Average Rate of Change} = \frac{f(0) - f(-2)}{0 - (-2)} = \frac{3 - (-1)}{0 + 2} = \frac{3 + 1}{2} = \frac{4}{2} = 2
\]

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