The degree of a polynomial function determines the end behavior of its graph. ... A rational function is a function of the form f(x)=P(x)Q(x), f ( x ) = P ( x ) Q ( x ) , where P(x) and Q(x) are both polynomials. A rational function f(x)=P(x)Q(x) f ( x ) = P ( x ) Q ( x ) may have a vertical asymptote whenever Q(x)=0.

Are all polynomials rational functions?

Note that every polynomial function is a rational function with Q(x)=1 Q ( x ) = 1 . A function that cannot be written in the form of a polynomial, such as f(x)=sin(x) f ( x ) = sin ⁡ , is not a rational function.

Why is a rational function not a polynomial?

Any rational function r(x) = , where q(x) is not the zero polynomial. ... Because by definition a rational function may have a variable in its denominator, the domain and range of rational functions do not usually contain all the real numbers.