given the function ( f(x)=-2x - 5 ).
find the average rate of change of ( f ) from ( x=-2 ) to ( x = 3 ).
give your answer as an integer or reduced fraction.
average rate of change:

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$ and $b = 3$.
## Step2: Calculate $f(-2)$
Substitute $x=-2$ into $f(x)=-2x^{2}-5$.
$$
\begin{align*}
f(-2)&=-2\times(-2)^{2}-5\
&=-2\times4 - 5\
&=-8-5\
&=-13
\end{align*}
$$
## Step3: Calculate $f(3)$
Substitute $x = 3$ into $f(x)=-2x^{2}-5$.
$$
\begin{align*}
f(3)&=-2\times3^{2}-5\
&=-2\times9-5\
&=-18 - 5\
&=-23
\end{align*}
$$
## Step4: Calculate the average rate of change
Substitute $f(-2)=-13$, $f(3)=-23$, $a=-2$, and $b = 3$ into the formula $\frac{f(b)-f(a)}{b - a}$.
$$
\begin{align*}
\frac{f(3)-f(-2)}{3-(-2)}&=\frac{-23-(-13)}{3 + 2}\
&=\frac{-23 + 13}{5}\
&=\frac{-10}{5}\
&=-2
\end{align*}
$$

# Answer:
$-2$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

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

Step3: Calculate \(f(3)\)

Step4: Calculate the average rate of change

Answer: