2v next post test: relationships between functions what is the approximate rate of change of this function…

Answer:

B. $-\frac{1}{2}$

Explanation:

Step1: Recall rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Identify $a$, $b$, $f(a)$ and $f(b)$

From the interval $[-2,2]$, $a=-2$, $b = 2$. By looking at the graph, when $x=-2$, $y\approx4$ (approximate value from the graph), so $f(-2)\approx4$. When $x = 2$, $y\approx - 4$ (approximate value from the graph), so $f(2)\approx-4$.

Step3: Calculate the rate of change

Substitute into the formula: $\frac{f(2)-f(-2)}{2-(-2)}=\frac{-4 - 4}{2+2}=\frac{-8}{4}=- \frac{1}{2}$.