Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -1 leq x leq 1 )?

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-1\) and \(b = 1\).

Step2: Find \(f(-1)\) and \(f(1)\) from the graph

From the graph, when \(x=-1\), \(f(-1)=15\) (by looking at the \(y\) - value corresponding to \(x =-1\)). When \(x = 1\), \(f(1)=10\) (by looking at the \(y\) - value corresponding to \(x = 1\)).

Step3: Substitute into the formula

Substitute \(a=-1\), \(b = 1\), \(f(a)=15\), and \(f(b)=10\) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{10-15}{1-(-1)}=\frac{-5}{2}=-2.5\)

Answer:

\(-2.5\)