Question

find the average rate of change for the following graph over the interval $-1\leq x\leq3$.

Explanation:

Step1: Recall the average rate of change formula

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 \(x=-1\), \(f(-1)=0\) (assuming the grid - based on visual inspection of the parabola). When \(x = 3\), \(f(3)=8\) (counting the units on the \(y\) - axis).

Step3: Substitute into the formula

Substitute \(a=-1\), \(b = 3\), \(f(a)=0\), \(f(b)=8\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{8-0}{3-(-1)}=\frac{8}{4}\).

Answer:

\(2\) (Option A)