Question

What is the fundamental difference in the algebraic representation of a polynomial function and a rational function? How do their graphs differ? To earn full credit be sure to address both parts to this question.

Answer 1

Polynomial function is a generic function in the form (linear, quadratic, cubic, and so on.)

Rational function is a function of two polynomial functions written as a fraction or quotient of two polynomial function in the form :

$f(x)=\frac{P(x)}{Q(x)}$

So the difference is rational function shows a quotient of two polynomial functions.

The graph of a polynomial function is continuous while the graph of a rational function is discontinuous as the denominator will become zero at some point. When the denominator is 0, the function will be undefined, thus resulting to a discontinuous graph.