Question

the graph of the function f, shown above, consists of three line segments. what is the average rate of change of f over the interval -1 ≤ x ≤ 6?

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-1\) and \(b = 6\).

Step2: Find \(f(-1)\) and \(f(6)\) from the graph

From the graph, when \(x=-1\), \(f(-1)=0\) (by observing the \(x\)-intercept - like behavior at \(x = - 1\)). When \(x = 6\), \(f(6)=0\) (the \(x\)-intercept).

Step3: Substitute into the formula

Substitute \(a=-1\), \(b = 6\), \(f(-1)=0\), and \(f(6)=0\) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{0-0}{6-(-1)}=\frac{0}{7}\).

Answer:

\(0\)