Calculate the average rate of change over the interval [3, 4] of the given graph of...

1. Identify the interval: The problem asks for the average rate of change over the interval $[3, 4]$. This means we need to consider the function's values at $x=3$ and $x=4$.

2. Determine the function values at the endpoints of the interval: From the graph, we can identify the coordinates of the two points given: $(3, 4)$ and $(4, 20)$.
- At $x=3$, the value of the function is $f(3) = 4$.
- At $x=4$, the value of the function is $f(4) = 20$.

3. Recall the formula for average rate of change: The average rate of change of a function $f(x)$ over an interval $[a, b]$ is given by the formula:
$$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$$

4. Substitute the values into the formula: In this case, $a=3$ and $b=4$. So, we have:
$$\text{Average Rate of Change} = \frac{f(4) - f(3)}{4 - 3}$$
Substitute the function values found in Step 2:
$$\text{Average Rate of Change} = \frac{20 - 4}{4 - 3}$$

5. Calculate the result: Perform the subtraction in the numerator and the denominator:
$$\text{Average Rate of Change} = \frac{16}{1}$$
$$\text{Average Rate of Change} = 16$$