Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -7leq xleq -5 )?

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, \(a=-7\) and \(b = - 5\).

Step2: Find \(f(-7)\) and \(f(-5)\) from the graph

From the graph, when \(x=-7\), \(y = f(-7)=4\) (since the point \((-7,4)\) lies on the graph). When \(x=-5\), \(y=f(-5)=14\) (since the point \((-5,14)\) lies on the graph).

Step3: Substitute values into the formula

Substitute \(a=-7\), \(b=-5\), \(f(a) = 4\), and \(f(b)=14\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{14 - 4}{-5-(-7)}=\frac{10}{2}\).

Answer:

\(5\)