Question

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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 \(y = f(x)\) on 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 \(x=-1\), \(y=-5\) (so \(f(-1)=-5\)), and when \(x = 1\), \(y = 15\) (so \(f(1)=15\)).

Step3: Substitute into the formula

Substitute \(a=-1\), \(b = 1\), \(f(-1)=-5\), and \(f(1)=15\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{15-(-5)}{1-(-1)}=\frac{15 + 5}{1+1}=\frac{20}{2}\).

Answer:

\(10\)