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?

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.