1. **State the problem:** Create a polynomial function of degree 4 with an odd leading coefficient and an even constant term. 2. **Form the polynomial function:** Given: $$3x^4 - 2x^3 + 5x^2 - 6x + 4$$ - Degree is 4 (highest power of $x$). - Leading coefficient is 3 (odd). - Constant term is 4 (even). 3. **Characteristics of the polynomial:** - Degree: 4 - Leading term: $$3x^4$$ - Leading coefficient: 3 - Constant term: 4 4. **Graph behavior description:** - Since the degree is even and the leading coefficient is positive, the ends of the graph rise to positive infinity as $$x \to \pm \infty$$. - The graph is smooth and continuous. - The graph crosses the y-axis at the constant term, which is 4. - The shape is a typical quartic curve opening upwards. 5. **Summary:** The polynomial $$3x^4 - 2x^3 + 5x^2 - 6x + 4$$ satisfies all conditions. Final answer: $$3x^4 - 2x^3 + 5x^2 - 6x + 4$$