calculate the average rate of change from ( x = - 2 ) to ( x = 1 ) of the function below.
( f ( x ) = x ^ { 2 } + 5 x - 12 )
first, find the change in ( y ) by evaluating the function at ( - 2 ) and ( 1 ):
( f ( - 2 ) = )
( f ( 1 ) = )
the change in ( y ) is

Question

Accepted Answer

# Explanation:
## Step1: Evaluate $f(-2)$
Substitute $x = - 2$ into $f(x)=x^{2}+5x - 12$:
$$
\begin{align*}
f(-2)&=(-2)^{2}+5\times(-2)-12\
&=4-10 - 12\
&=-18
\end{align*}
$$
## Step2: Evaluate $f(1)$
Substitute $x = 1$ into $f(x)=x^{2}+5x - 12$:
$$
\begin{align*}
f(1)&=1^{2}+5\times1-12\
&=1 + 5-12\
&=-6
\end{align*}
$$
## Step3: Calculate the change in $y$
The change in $y$ is $f(1)-f(-2)$.
$$
\begin{align*}
f(1)-f(-2)&=-6-(-18)\
&=-6 + 18\
&=12
\end{align*}
$$

# Answer:
$f(-2)=-18$, $f(1)=-6$, the change in $y$ is $12$

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QUESTION IMAGE

Question

Explanation:

Step1: Evaluate \(f(-2)\)

Step2: Evaluate \(f(1)\)

Step3: Calculate the change in \(y\)

Answer: