using the function graph shown below, calculate the average rate of change from (2, -1) to (6, 1).

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The formula for the average rate of change of a function $y = f(x)$ from $x_1$ to $x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.
## Step2: Identify the values of $x_1,x_2,f(x_1),f(x_2)$
Given the points $(x_1,y_1)=(2,-1)$ and $(x_2,y_2)=(6,1)$, so $x_1 = 2$, $x_2=6$, $f(x_1)=-1$, $f(x_2) = 1$.
## Step3: Substitute the values into the formula
$$
\begin{align*}
\frac{f(x_2)-f(x_1)}{x_2 - x_1}&=\frac{1-(-1)}{6 - 2}\
&=\frac{1 + 1}{4}\
&=\frac{2}{4}\
&=\frac{1}{2}
\end{align*}
$$

# Answer:
$\frac{1}{2}$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Identify the values of \(x_1,x_2,f(x_1),f(x_2)\)

Step3: Substitute the values into the formula

Answer: