Question

use the graph below to find the average rate of change of the function on the interval 0,5.

Explanation:

Step1: Recall average rate of change formula

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 \( b = 5 \).

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

From the graph, when \( x = 0 \), the \( y \)-value (which is \( f(0) \)) is 5. So, \( f(0)=5 \).

Step3: Find \( f(5) \) from the graph

From the graph, when \( x = 5 \), the \( y \)-value (which is \( f(5) \)) is 0 (since the graph intersects the \( x \)-axis at \( x = 5 \)). So, \( f(5)=0 \).

Step4: Calculate the average rate of change

Substitute \( a = 0 \), \( b = 5 \), \( f(0)=5 \), and \( f(5)=0 \) into the formula:

$$ \frac{f(5)-f(0)}{5 - 0}=\frac{0 - 5}{5}=\frac{-5}{5}=-1 $$

Answer:

\(-1\)