https://file.aiquickdraw.com/mathbot/file/172820143704210j33x6h.jpg

The given function is:

\[
f(x) = x^{1/3} - 2x + 1
\]

### To determine if this is a polynomial:
- A polynomial function consists of terms with non-negative integer exponents of the variable \(x\).
- In this function, the exponent of the first term is \( \frac{1}{3} \), which is a fractional exponent. This violates the condition that all exponents must be non-negative integers.

### Conclusion:
This function is **not a polynomial** because the term \(x^{1/3}\) has a fractional exponent.

Would you like further explanation or have any questions?

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Here are 5 related questions to explore:
1. What are the conditions for a function to be considered a polynomial?
2. How do we find the degree of a polynomial?
3. Can a function with a negative exponent ever be a polynomial?
4. How does the degree of a polynomial affect its graph?
5. What is the difference between polynomial and non-polynomial functions?

**Tip:** Always check the exponents in a function to determine if it's a polynomial—these must be non-negative integers.

Determine if the following function is a polynomial function. If it is, identify the degree. f(x) = x^(1/3) - 2x + 1

Learn how to determine whether the function f(x) = x^(1/3) - 2x + 1 is a polynomial. Understand key algebraic concepts, including what defines a polynomial and why fractional exponents violate this definition. Suitable for high school students in Grades 9-12.

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