1. **State the problem:** We need to find the end behavior of the polynomial function $$f(x) = 3x^4 - 63x^2 + 6x^3 + 120 - 66x$$. 2. **Recall the rule for end behavior of polynomials:** The end behavior of a polynomial function is determined by its leading term, which is the term with the highest power of $x$. 3. **Identify the leading term:** The leading term here is $$3x^4$$ because $x^4$ has the highest exponent. 4. **Analyze the leading term:** Since the coefficient $3$ is positive and the degree $4$ is even, the end behavior is: - As $x \to \infty$, $f(x) \to \infty$ - As $x \to -\infty$, $f(x) \to \infty$ 5. **Conclusion:** The function rises to positive infinity on both ends. **Final answer:** - As $x \to \infty$, $y \to \infty$ - As $x \to -\infty$, $y \to \infty$