Question

(03.04)
estimate the average rate of change between ( x = 0 ) and ( x = 2 ) for the function shown

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, \(a = 0\) and \(b=2\).

Step2: Estimate \(f(0)\) and \(f(2)\) from the graph

From the graph, when \(x = 0\), \(f(0)\approx - 6\). When \(x = 2\), \(f(2)\approx 6\).

Step3: Calculate the average rate of change

Substitute into the formula: \(\frac{f(2)-f(0)}{2-0}=\frac{6-(-6)}{2}=\frac{6 + 6}{2}=\frac{12}{2}=6\)

Answer:

A. 6