# How can you tell whether a function is rational or not? How do you determine holes of a graph?

## Question:

How can you tell whether a function is rational or not?

How do you determine holes of a graph?

## Rational function

In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.

A function is rational if it is in the form of {eq}f(x)=\frac{g(x)}{h(x)} {/eq}

A rational function is any function that can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.

Illustration:

$$f(x)=\frac{3x^{2}}{2x+1}$$

If it is not in the form {eq}f(x)=\frac{g(x)}{h(x)} {/eq} therefore it is not a rational function.

We define holes in the graph as a discontinuity of a function.

This is most often the value of the function that will make it undefined.

Example:

$$f(x)=\frac{3x^{2}}{2x+1}$$

The function given above is discontinuous at {eq}x=-\frac{1}{2} {/eq} because if we substitute the value x the function will be undefined.