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 = -9 to x = -5. 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, \(a=-9\) and \(b=-5\).

Step2: Find \(g(-9)\) and \(g(-5)\) from the graph

From the graph, when \(x=-9\), \(g(-9)=1\); when \(x = -5\), \(g(-5)=-5\).

Step3: Substitute values into the formula

Substitute \(a=-9\), \(b=-5\), \(g(a) = 1\), and \(g(b)=-5\) into \(\frac{g(b)-g(a)}{b - a}\).

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Answer:

\(-\frac{3}{2}\)