https://file.aiquickdraw.com/mathbot/file/1728310437119b8uo8rzr.jpg

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.

Select which of the following are polynomial functions.

Learn how to identify polynomial functions by analyzing their graphs. This problem involves recognizing key characteristics of quadratic and cubic functions, such as smoothness and the absence of asymptotes. Suitable for high school students (Grades 9-12).

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