Let's analyze each of the graphs to determine which represent polynomial functions.

1. Top left (Green graph): The graph appears to represent an absolute value function, which has a sharp vertex. Polynomial functions are smooth and continuous without sharp turns. Therefore, this is not a polynomial function.

2. Top right (Orange graph): This graph has a vertical asymptote, indicating a rational function (likely of the form $\frac{1}{x}$), not a polynomial. Polynomials do not have asymptotes, so this is not a polynomial function.

3. Bottom left (Blue graph): This graph is a parabola, which is a quadratic function ($f(x) = ax^2 + bx + c$). Quadratics are polynomials of degree 2, so this is a polynomial function.

4. Bottom right (Red graph): This graph appears to be a cubic function ($f(x) = ax^3 + bx^2 + cx + d$), which is a polynomial of degree 3. Therefore, this is a polynomial function.

Summary:

• Polynomial functions: Bottom left (blue), Bottom right (red).
• Not polynomial functions: Top left (green), Top right (orange).

Would you like further details on any of these graphs or concepts?

Here are five questions to expand on this:

1. What makes a polynomial function smooth and continuous?
2. How can you identify a rational function by its graph?
3. Can an absolute value function ever be a polynomial function?
4. How do the degrees of polynomials affect their graph shapes?
5. What are the key differences between polynomial and non-polynomial functions?

Tip: Polynomial functions are defined by their smooth curves and absence of sharp turns or asymptotes.