Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -5 leq x leq 0 )?

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, \(a=-5\) and \(b = 0\).

Step2: Find \(f(-5)\) and \(f(0)\) from the graph

From the graph, when \(x=-5\), \(y = f(-5)=4\) (by looking at the \(y\) - coordinate of the point on the graph with \(x=-5\)). When \(x = 0\), \(y=f(0)=-10\) (by looking at the \(y\) - coordinate of the point on the graph with \(x = 0\)).

Step3: Substitute values into the formula

Substitute \(a=-5\), \(b = 0\), \(f(a)=4\), and \(f(b)=-10\) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-10 - 4}{0-(-5)}=\frac{-14}{5}=-2.8\).

Answer:

\(-2.8\)