Question

What is the fundamental difference in the algebraic representation of a polynomial function and a rational function? How do you the graphs differ?

Answer 1

The difference between polynomial functions and rational functions is that the the last, the rational functions, can be always expressed as a quotient of polynomials.

This will make them differ in the graphs: as in rational functions we will have a polynomial in the denominator, its roots will become discontinuities (holes or vertical asymptotes). They may also present horizontal or slant asymptotes.