Question

find the average rate of change for the following graph over the interval $-1\leq x\leq 3$.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-1\) and \(b = 3\).

Step2: Find \(f(-1)\) and \(f(3)\) from the graph

From the graph, when \(x=-1\), \(f(-1)=0\); when \(x = 3\), \(f(3)=4\).

Step3: Substitute into the formula

Substitute \(a=-1\), \(b = 3\), \(f(-1)=0\), and \(f(3)=4\) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{4-0}{3-(-1)}=\frac{4}{4}=1\).

Answer:

B. 1