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