Here’s a graph that illustrates the function $f(x)$ based on the conditions provided:

• The function decreases on $(-\infty, -5)$, reaching a minimum at $x = -5$.
• It increases from $x = -5$ to $x = 3$.
• At $x = 3$, there’s a cusp, and the function starts decreasing again for $x > 3$.

Would you like a detailed explanation of any of the sections or have any specific questions?

Here are related questions to deepen your understanding:

1. What types of critical points are commonly seen on graphs, and how do they affect the shape?
2. How can you determine the existence of a cusp or vertical tangent based on the derivative?
3. Why does a sign change in the derivative indicate increasing or decreasing behavior?
4. What are examples of functions with cusps and vertical tangents?
5. How can you approximate the graph of a derivative based on the original function?

Tip: To identify critical points and behavior changes, analyze where the derivative equals zero or is undefined.