To find the average rate of change of a function over a given interval, we use the formula:

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

where $a$ and $b$ are the endpoints of the interval, in this case, $3.5 \leq x \leq 4$.

The problem requires us to determine the average rate of change from the graph of the function on the interval $[3.5, 4]$. However, since I can't see the actual graph, I will describe the process you would follow:

1. Identify $f(3.5)$ and $f(4)$ from the graph, i.e., the values of the function at $x = 3.5$ and $x = 4$.
2. Subtract $f(3.5)$ from $f(4)$ to find the difference in $y$-values over this interval.
3. Divide this difference by $4 - 3.5 = 0.5$ to get the average rate of change.

Given that the answer selected is $2$, it suggests that:

$\frac{f(4) - f(3.5)}{0.5} = 2$

Thus, $f(4) - f(3.5) = 2 \times 0.5 = 1$.

If you need further clarification or would like me to explain how to estimate points on a graph, feel free to ask!

Here are some follow-up questions to explore this concept further:

1. How do you interpret the average rate of change in real-world scenarios?
2. What would the average rate of change be if $f(x)$ were a constant function over the interval?
3. How can you visually estimate the rate of change from a graph without exact points?
4. How does the interval length affect the average rate of change?
5. Can you calculate the rate of change over an interval if only the slope is given?

Tip: For a visual representation, draw a secant line connecting the points at $x = 3.5$ and $x = 4$ on the graph. The slope of this line represents the average rate of change over the interval.