Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -4 leq x leq -3 )?

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-4\) and \(b = - 3\).

Step2: Find \(f(-4)\) and \(f(-3)\) from the graph

From the graph, when \(x=-4\), \(y=-80\) (so \(f(-4)=-80\)), and when \(x = - 3\), \(y = 60\) (so \(f(-3)=60\)).

Step3: Substitute into the formula

Substitute \(a=-4\), \(b=-3\), \(f(a)=-80\), and \(f(b)=60\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{60-(-80)}{-3-(-4)}=\frac{60 + 80}{-3 + 4}\).

Step4: Simplify the expression

\(\frac{60+80}{-3 + 4}=\frac{140}{1}=140\).

Answer:

\(140\)