The graph shown represents a polynomial function. The question asks for the end behavior of the function $f(x)$, which refers to how the function behaves as $x \to \infty$ (towards positive infinity) and $x \to -\infty$ (towards negative infinity).

From the graph:

• As $x \to \infty$ (towards the right), the graph decreases towards $-\infty$.
• As $x \to -\infty$ (towards the left), the graph also decreases towards $-\infty$.

End Behavior:

• As $x \to \infty$, $f(x) \to -\infty$.
• As $x \to -\infty$, $f(x) \to -\infty$.

This type of end behavior suggests that the polynomial has an odd degree (because the ends go in the same direction) and the leading coefficient is negative (since the ends are both going down).

Would you like any further details or have any questions on this?

Here are 5 related questions:

1. What does the degree of a polynomial tell you about the end behavior?
2. How can the leading coefficient affect the shape of the graph?
3. Can the graph of a polynomial ever cross the x-axis more times than its degree?
4. How do we determine if a polynomial has symmetry (even or odd functions)?
5. What does the number of turning points on a graph tell you about its degree?

Tip: The number of turning points (peaks or valleys) of a polynomial function is always less than or equal to its degree minus 1.