Question: The graph of a function $f$ is shown below. Use the graph of the function to find its average rate of change from $x = 3$ to $x = 4$ . Simplify your answer as much as possible.

1. **State the problem:** We need to find the average rate of change of the function $f$ from $x=3$ to $x=4$ using the graph. 2. **Formula for average rate of change:** $$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$$ where $a=3$ and $b=4$. 3. **Find $f(3)$ and $f(4)$ from the graph:** - From the graph, locate the point where $x=3$ and read the corresponding $y$-value $f(3)$. - Similarly, locate the point where $x=4$ and read the corresponding $y$-value $f(4)$. 4. **Calculate the difference in function values:** $$f(4) - f(3)$$ 5. **Calculate the difference in $x$ values:** $$4 - 3 = 1$$ 6. **Compute the average rate of change:** $$\frac{f(4) - f(3)}{4 - 3} = \frac{f(4) - f(3)}{1} = f(4) - f(3)$$ 7. **Simplify the result:** The average rate of change is simply the difference in $y$-values between $x=4$ and $x=3$. **Note:** Since the exact $y$-values are not provided in the text, you must read them from the graph to complete the calculation. **Final answer:** $$\text{Average rate of change} = f(4) - f(3)$$ Replace $f(3)$ and $f(4)$ with their values from the graph to get the numerical answer.