Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval 3 ≤ x ≤ 4?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 3$ and $b = 4$.

Step2: Read function values from graph

From the graph, when $x = 3$, assume $f(3)=- 4$ (by looking at the $y$ - value of the graph at $x = 3$). When $x = 4$, assume $f(4)=2$ (by looking at the $y$ - value of the graph at $x = 4$).

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(4)-f(3)}{4 - 3}=\frac{2-(-4)}{1}=\frac{2 + 4}{1}=6$.

Answer:

6