Question

the graph of a function f is shown below.
use the graph of the function to find its average rate of change from x = -5 to x = -2.
simplify your answer as much as possible.

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-5\) and \(b = - 2\).

Step2: Find \(f(-5)\) and \(f(-2)\) from the graph

From the graph, when \(x=-5\), \(f(-5)=-2\); when \(x = - 2\), \(f(-2)=-2\).

Step3: Substitute into the formula

Substitute \(a=-5\), \(b=-2\), \(f(a)=-2\), and \(f(b)=-2\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-2-(-2)}{-2-(-5)}=\frac{-2 + 2}{-2 + 5}\).

Step4: Simplify the expression

\(\frac{-2 + 2}{-2 + 5}=\frac{0}{3}=0\).

Answer:

\(0\)