Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function on interval ( -1 leq x leq 0 )?

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, \(a=-1\) and \(b = 0\).

Step2: Find \(f(-1)\) and \(f(0)\) from the graph

From the graph, when \(x=-1\), \(f(-1)=40\) (by observing the \(y -\) value corresponding to \(x =-1\)). When \(x = 0\), \(f(0)=20\) (by observing the \(y -\) value corresponding to \(x = 0\)).

Step3: Substitute into the formula

Substitute \(a=-1\), \(b = 0\), \(f(a)=40\), and \(f(b)=20\) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{20-40}{0-(-1)}=\frac{-20}{1}=-20\).

Answer:

\(-20\)