Question

question
the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -9 leq x leq -8 )?
answer

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-9\) and \(b = - 8\).

Step2: Find \(f(-9)\) and \(f(-8)\) from the graph

From the graph, when \(x=-9\), \(y=-40\) (so \(f(-9)=-40\)), and when \(x = - 8\), \(y = 40\) (so \(f(-8)=40\)).

Step3: Substitute into the formula

Substitute \(a=-9\), \(b=-8\), \(f(a)=-40\), and \(f(b)=40\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{40-(-40)}{-8-(-9)}=\frac{40 + 40}{-8 + 9}\).

Step4: Simplify the expression

\(\frac{80}{1}=80\).

Answer:

\(80\)