Question: The graph of a function $f$ is shown below.
Use the graph of the function to find its average rate of change from $x = 0$ to $x = 3$.
Simplify your answer as much as possible.
Graph: Exponential curve in the center-left of the page, with plotted points at $(0, 1)$, $(1, 2)$, $(2, 4)$, and $(3, 8)$; position_hint = center.
1. **State the problem:** We need to find the average rate of change of the function $f$ from $x=0$ to $x=3$ using the given points on the graph.
2. **Recall the formula for average rate of change:**
$$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$$
where $a=0$ and $b=3$.
3. **Identify the function values at the given points:**
From the graph, $f(0) = 1$ and $f(3) = 8$.
4. **Substitute the values into the formula:**
$$\frac{f(3) - f(0)}{3 - 0} = \frac{8 - 1}{3 - 0} = \frac{7}{3}$$
5. **Simplify the fraction:**
$$\frac{7}{3}$$ is already in simplest form.
6. **Interpretation:** The average rate of change of the function $f$ from $x=0$ to $x=3$ is $\frac{7}{3}$, meaning on average, the function increases by $\frac{7}{3}$ units for each unit increase in $x$ over this interval.