Which of the following functions are polynomial functions? Select all that apply.
\[
f(x)=x^{18}-5
\]
$f(x)=x^{2}+x+x^{-1}$
$f(x)=1+x+x^{4}$
$f(x)=3 x^{\frac{1}{3}}+x^{\frac{1}{2}}-7$
$f(x)=x^{3}+6 x^{2}+x+13$

Step 1 ：Given the functions, we need to identify which ones are polynomial functions.

Step 2 ：A polynomial function is a function that can be expressed in the form of a polynomial. The general form of a polynomial function is \(f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0\), where \(a_n, a_{n-1}, ..., a_2, a_1, a_0\) are constants and \(n\) is a non-negative integer.

Step 3 ：Looking at the given functions, we can see that the function \(f(x)=x^{18}-5\) fits the definition of a polynomial function because it can be expressed in the form of a polynomial and the exponent of \(x\) is a non-negative integer.

Step 4 ：Thus, the function \(f(x)=x^{18}-5\) is a polynomial function.