Which of the following functions is not polynomial?

A polynomial function is defined as a function that can be expressed in the form of ( ax^n + bx^{n-1} + ... + k ), where ( a, b, k ) are constants, ( n ) is a non-negative integer, and ( x ) is a variable. The key characteristics of polynomial functions are that they involve only non-negative integer powers of ( x ) and do not contain any division by ( x ) or taking roots of ( x ).

Looking at the given functions, the function ( y = 1/x ) stands out because it involves a division by the variable ( x ). This can be rewritten as ( y = x^{-1} ), which means it includes a negative exponent. Since negative exponents do not conform to the non-negative integer requirement of polynomial functions, this function is not a polynomial.

In contrast, the other functions provided—( y = 2x^3 + 5x ), ( y = x^2 - 4 ), and ( y = -3x + 1 )—are all composed of terms that fit the definition of a polynomial. They each involve only non-negative integer exponents and constants. As