The graph provided represents the function $y = f(x)$. To determine the end behavior of $f(x)$, we analyze what happens to $f(x)$ as $x \to \infty$ (positive infinity) and as $x \to -\infty$ (negative infinity).

From the graph:

1. As $x \to -\infty$, the function $f(x) \to -\infty$. The graph decreases without bound on the far left.
2. As $x \to \infty$, the function $f(x) \to \infty$. The graph increases without bound on the far right.

Conclusion:

The end behavior of $f(x)$ is:

• $\lim_{x \to -\infty} f(x) = -\infty$
• $\lim_{x \to \infty} f(x) = \infty$

This is consistent with the behavior of a cubic polynomial with a positive leading coefficient. The general shape suggests $f(x)$ is an odd-degree polynomial with positive growth on the right and negative growth on the left.

Would you like a detailed explanation of how to determine end behavior from graphs or additional analysis of the polynomial's degree and leading term?

Related Questions:

1. How do you determine the degree of a polynomial from its graph?
2. What are the key characteristics of odd-degree polynomials?
3. How do turning points relate to the degree of a polynomial?
4. How does the leading coefficient affect the end behavior of a polynomial?
5. Can you explain symmetry in graphs and how it relates to polynomial functions?

Tip:

When analyzing end behavior, focus on the graph's far-left and far-right trends, as these are dictated by the highest-degree term of the polynomial.