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determine the average rate of change of the function h(x) = 3x² + 2x - 7 over the interval -2, 2.
10
2
-10
-2

Question

Accepted Answer

# Explanation:
## Step1: Recall the average rate of change formula
The average rate of change of a function $ h(x) $ over the interval $[a, b]$ is given by $\frac{h(b) - h(a)}{b - a}$. Here, $ a=-2 $ and $ b = 2 $.

## Step2: Calculate $ h(-2) $
Substitute $ x=-2 $ into $ h(x)=3x^{2}+2x - 7 $:
$$
\begin{align*}
h(-2)&=3(-2)^{2}+2(-2)-7\
&=3(4)-4 - 7\
&=12-4 - 7\
&=1
\end{align*}
$$

## Step3: Calculate $ h(2) $
Substitute $ x = 2 $ into $ h(x)=3x^{2}+2x - 7 $:
$$
\begin{align*}
h(2)&=3(2)^{2}+2(2)-7\
&=3(4)+4 - 7\
&=12 + 4-7\
&=9
\end{align*}
$$

## Step4: Apply the average rate of change formula
Now, use $\frac{h(2)-h(-2)}{2-(-2)}$:
$$
\begin{align*}
\frac{h(2)-h(-2)}{2-(-2)}&=\frac{9 - 1}{2 + 2}\
&=\frac{8}{4}\
&=2
\end{align*}
$$

# Answer:
2

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \( h(-2) \)

Step3: Calculate \( h(2) \)

Step4: Apply the average rate of change formula

Answer: