#### Answer

$\text{Not a polynomial function because it has a term with a non-integer power or degree.}$

#### Work Step by Step

$\text{A polynomial function is a function of the form}$
$$f(x)=a_n x^n +a_{n-1} x^{n-1}+...+a_1 x+ a_0$$
Where the coefficients $(a_n, a_{n-1}.....)$ are real numbers and $n$ is a non-negative integer
The term $x^{\frac{3}{2}}$ has a non-integer power, therefore the function isn't a polynomial.