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 -4 )?

Explanation:

Step1: Identify the formula for average rate of change

The formula for 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 \(b = - 4\).

Step2: Find \(f(-9)\) and \(f(-4)\) from the graph

From the graph, when \(x=-9\), \(y=-16\) (so \(f(-9)=-16\)), and when \(x = - 4\), \(y=-4\) (so \(f(-4)=-4\)).

Step3: Substitute values into the formula

Substitute \(a=-9\), \(b=-4\), \(f(a)=-16\), and \(f(b)=-4\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-4-(-16)}{-4-(-9)}=\frac{-4 + 16}{-4 + 9}=\frac{12}{5}=2.4\).

Answer:

\(2.4\)