Question

question the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( 0 leq x leq 4 )?

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) on the interval \( [a, b] \) is given by \( \frac{f(b) - f(a)}{b - a} \). Here, \( a = 0 \) and \( b = 4 \), so we need to find \( f(0) \) and \( f(4) \) from the graph.

Step2: Find \( f(0) \) from the graph

Looking at the graph, when \( x = 0 \), the \( y \)-value (which is \( f(0) \)) is 8. So \( f(0)=8 \).

Step3: Find \( f(4) \) from the graph

Looking at the graph, when \( x = 4 \), the \( y \)-value (which is \( f(4) \)) is 2. So \( f(4)=2 \).

Step4: Calculate the average rate of change

Using the formula \( \frac{f(4)-f(0)}{4 - 0} \), substitute \( f(4)=2 \), \( f(0)=8 \), and \( 4 - 0 = 4 \). So we have \( \frac{2 - 8}{4}=\frac{-6}{4}=-\frac{3}{2}=-1.5 \).

Answer:

\(-\frac{3}{2}\) (or \(-1.5\))