The graph provided represents a polynomial function, and the question asks about the end behavior of the function $f(x)$.

Identifying the end behavior:

• The end behavior of a function describes how the function behaves as $x$ approaches $\infty$ (positive infinity) and $-\infty$ (negative infinity).
• From the graph:
  • As $x \to \infty$, the graph goes upwards, meaning $y \to \infty$.
  • As $x \to -\infty$, the graph also goes upwards, meaning $y \to \infty$.

This indicates that the polynomial is of even degree with a positive leading coefficient (because both ends of the graph are going up).

Correct answer:

• As $x \to -\infty$, $y \to \infty$
• As $x \to \infty$, $y \to \infty$

Therefore, the correct choice is:

• As $x \to -\infty$, $y \to \infty$ and as $x \to \infty$, $y \to \infty$.

Would you like more details or have any other questions?

Here are some related questions to deepen your understanding:

1. How can you determine the degree of a polynomial from its graph?
2. What does the leading coefficient test say about the end behavior of polynomials?
3. How does the number of turning points relate to the degree of a polynomial?
4. What is the significance of the roots or x-intercepts in the graph of a polynomial?
5. How do you use the symmetry of the graph to determine if the function is even or odd?

Tip: The end behavior of polynomials depends only on the degree and the sign of the leading coefficient.