To determine the average rate of change of the graph over the interval $[2,18]$, we use the formula for the average rate of change of a function:

$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$

Where:

• $a = 2$ and $b = 18$ are the endpoints of the interval.
• $f(a)$ is the value of the function at $x = 2$, and $f(b)$ is the value of the function at $x = 18$.

Step 1: Find $f(2)$ and $f(18)$ from the graph

1. At $x = 2$, the value of $f(2)$ is approximately 0.
2. At $x = 18$, the value of $f(18)$ is approximately 18.

Step 2: Apply the formula

Substitute $a = 2$, $b = 18$, $f(2) = 0$, and $f(18) = 18$:

$\text{Average Rate of Change} = \frac{f(18) - f(2)}{18 - 2}$

$\text{Average Rate of Change} = \frac{18 - 0}{18 - 2} = \frac{18}{16} = 1.125$

Final Answer:

The average rate of change of the graph over the interval $[2,18]$ is 1.125.

Let me know if you'd like me to explain this further or solve similar problems.

Related Questions:

1. How is the average rate of change related to the slope of a line?
2. What is the difference between instantaneous rate of change and average rate of change?
3. How would the average rate of change differ if we used a smaller interval?
4. Can you calculate the average rate of change for a specific sub-interval, such as $[2, 10]$?
5. How does the behavior of the graph (increasing/decreasing) affect the average rate of change?

Tip:

The average rate of change gives you the slope of the straight line connecting two points on a curve, also known as the secant line.