Question 316563
Yes, it's fancy but it does have to be defined somehow.
{{{f(x)=3x^3+9x+5}}} is a polynomial. All of the exponents of the variable terms are non-negative integers (3,1,0).
{{{g(x)=2y^1.5+1/y}}} is not a polynomial. The exponents are 1.5 and -1 which violates the definition. 
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Yes, a rational function is basically the division of two polynomials.