Question

the graph of a function g is shown below. use the graph of the function to find its average rate of change from x = -6 to x = -4. 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 \(y = g(x)\) from \(x=a\) to \(x = b\) is given by \(\frac{g(b)-g(a)}{b - a}\). Here, \(a=-6\) and \(b = - 4\).

Step2: Find \(g(-6)\) and \(g(-4)\) from the graph

From the graph, when \(x=-6\), \(g(-6)=1\); when \(x=-4\), \(g(-4)=2\).

Step3: Substitute into the formula

Substitute \(a=-6\), \(b=-4\), \(g(-6) = 1\), and \(g(-4)=2\) into \(\frac{g(b)-g(a)}{b - a}\). We get \(\frac{g(-4)-g(-6)}{-4-(-6)}=\frac{2 - 1}{-4 + 6}\).

Step4: Simplify the expression

\(\frac{2-1}{-4 + 6}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)