Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-6 leq x leq 4$?

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, \(a=-6\) and \(b = 4\).

Step2: Find \(f(-6)\) and \(f(4)\) from the graph

From the graph, when \(x=-6\), \(y = f(-6)=6\) (by looking at the \(y\) - coordinate of the point on the graph at \(x =-6\)). When \(x = 4\), \(y=f(4)=0\) (by looking at the \(y\) - coordinate of the point on the graph at \(x = 4\)).

Step3: Substitute into the formula

Substitute \(a=-6\), \(b = 4\), \(f(a)=6\), and \(f(b)=0\) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{0 - 6}{4-(-6)}=\frac{-6}{4 + 6}\).

Step4: Simplify the expression

\(\frac{-6}{10}=-\frac{3}{5}=-0.6\)

Answer:

\(-0.6\)