To analyze the end behavior of the function $f(x)$ shown in the graph:

Observing the Graph:

• As $x \to +\infty$ (to the right), the function $f(x)$ increases without bound, i.e., $f(x) \to +\infty$.
• As $x \to -\infty$ (to the left), the function $f(x)$ decreases without bound, i.e., $f(x) \to -\infty$.

Conclusion:

• End behavior as $x \to +\infty$: $f(x) \to +\infty$
• End behavior as $x \to -\infty$: $f(x) \to -\infty$

This is characteristic of an odd-degree polynomial with a positive leading coefficient, likely a cubic function or higher odd degree.

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. What is the significance of end behavior in determining the degree of a polynomial?
2. How can you tell if the leading coefficient of a polynomial is positive or negative based on the graph?
3. What are the turning points of this graph, and how do they relate to the degree of the function?
4. How can we determine the exact degree of the polynomial from this graph?
5. What other features of the graph (like intercepts) help in constructing a potential equation for $f(x)$?

Tip: To determine the degree of a polynomial from its graph, count the number of turning points. A polynomial of degree $n$ can have at most $n-1$ turning points.