1. **State the problem:** Define what a polynomial function is. 2. **Explanation:** A polynomial function involves variables raised to non-negative integer powers combined using addition, subtraction, and multiplication. It does not include variables with negative or fractional exponents. 3. **Answer:** The correct choice is **d. A function that involves variables raised to non-negative integer powers**. 4. **State the problem:** Determine the end behavior of the polynomial function $h(x) = -2x^3 + 3x^2 + 12x$. 5. **Explanation:** The leading term $-2x^3$ dominates the end behavior. Since the degree is odd (3) and the leading coefficient is negative (-2), as $x \to \infty$, $h(x) \to -\infty$ (falls to the right), and as $x \to -\infty$, $h(x) \to \infty$ (rises to the left). 6. **Answer:** The correct choice is **b. Falls to the left and rises to the right**. 7. **State the problem:** How does the number of real roots relate to the degree of a polynomial? 8. **Explanation:** A polynomial of degree $n$ can have up to $n$ real roots, but the actual number can be less due to complex roots. Therefore, the number of real roots can be greater than, equal to, or less than the degree. 9. **Answer:** The correct choice is **d. The number of real roots can be greater than, equal to, or less than the degree of the polynomial**. 10. **State the problem:** Juliet's task with the function $f(x) = 2x^3 - 5x^2 + 4x + 1$. 11. **Explanation:** Juliet is asked to graph the function, which involves plotting points, analyzing shape, and noting intercepts. 12. **Answer:** The correct choice is **c. Sketch the graph of the function on a coordinate**. **Final answers:** 1. d 2. b 3. d 4. c