1. **State the problem:** Find the horizontal asymptote(s) of the function $$f(x) = \frac{3x^4 + 4x + 4}{2x^4 + 3x - 3}$$. 2. **Recall the rule for horizontal asymptotes:** - If the degrees of numerator and denominator are equal, the horizontal asymptote is $$y = \frac{\text{leading coefficient of numerator}}{\text{leading coefficient of denominator}}$$. - If degree numerator < degree denominator, horizontal asymptote is $$y=0$$. - If degree numerator > degree denominator, no horizontal asymptote. 3. **Identify degrees:** - Degree numerator = 4 (from $$3x^4$$) - Degree denominator = 4 (from $$2x^4$$) 4. **Apply the rule for equal degrees:** $$y = \frac{3}{2}$$ 5. **Conclusion:** The function has one horizontal asymptote at $$y = \frac{3}{2}$$. **Final answer:** $$y = \frac{3}{2}$$