Question

given the graph of f(x) below. determine the average rate of change of f(x) from x = - 2 to x = 2. give your answer as a simplified fraction if necessary. for example, if you found that m = 1/2, you would enter 1/2

Explanation:

Step1: Recall average - rate - of - change formula

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 $b = 2$.

Step2: Estimate function values from graph

By looking at the graph, assume $f(-2)\approx - 2$ and $f(2)\approx - 5$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(2)-f(-2)}{2-(-2)}=\frac{-5-( - 2)}{2 + 2}=\frac{-5 + 2}{4}=\frac{-3}{4}$.

Answer:

$-\frac{3}{4}$