# Characteristics of rational expressions

Contents

- 1 What are the characteristics of a rational function?
- 2 How do you identify rational expressions?
- 3 What is rational expression?
- 4 What is the most distinct characteristic of a rational function?
- 5 What is rational function in your own words?
- 6 How do you find the characteristics of a rational function?
- 7 How can you tell if a graph is a rational function?
- 8 How do you write a rational expression?
- 9 What are holes in rational functions?
- 10 How do you determine end behavior?
- 11 What is the horizontal asymptote of a rational function?
- 12 How do you find holes in rational functions?
- 13 How do you tell the difference between a hole and an asymptote?

## What are the characteristics of a rational function?

A

**rational function**is defined as the quotient of polynomials in which the denominator has a degree of at least 1 . In other words, there must be a variable in the denominator. The general form of a**rational function**is p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 .## How do you identify rational expressions?

**Rational expressions**are fractions containing polynomials. They can be simplified much like numeric fractions. To simplify a

**rational expression**, first

**determine**common factors of the numerator and denominator, and then remove them by rewriting them as

**expressions**equal to 1.

## What is rational expression?

A

**rational expression**is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.## What is the most distinct characteristic of a rational function?

One of the main

**characteristics**of**rational functions**is the existence of asymptotes. An asymptote is a straight line to which the graph of the**function**gets arbitrarily close. Typically one can classify the asymptotes into two types.## What is rational function in your own words?

A

**rational function**is any**function**which can be written as the ratio of two**polynomial functions**, where the**polynomial**in the denominator is not equal to zero. The domain of f(x)=P(x)Q(x) f ( x ) = P ( x ) Q ( x ) is the set of all points x for which the denominator Q(x) is not zero.## How do you find the characteristics of a rational function?

## How can you tell if a graph is a rational function?

## How do you write a rational expression?

To

**write a rational expression**in lowest terms, we must first find all common factors (constants, variables, or polynomials) or the numerator and the denominator. Thus, we must factor the numerator and the denominator. Once the numerator and the denominator have been factored, cross out any common factors.## What are holes in rational functions?

**Hole**A

**hole**exists on the graph of a

**rational function**at any input value that causes both the numerator and denominator of the

**function**to be equal to zero. They occur when factors can be algebraically canceled from

**rational functions**. Removable discontinuityRemovable discontinuities are also known as

**holes**.

## How do you determine end behavior?

The

**end behavior**of a polynomial function is the**behavior**of the graph of f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function**determine**the**end behavior**of the graph.## What is the horizontal asymptote of a rational function?

The

**horizontal asymptote of a rational function**can be determined by looking at the degrees of the numerator and denominator. Degree of numerator is less than degree of denominator:**horizontal asymptote**at y = 0. Degree of numerator is greater than degree of denominator by one: no**horizontal asymptote**; slant**asymptote**.## How do you find holes in rational functions?

## How do you tell the difference between a hole and an asymptote?

**Holes**occur when factors from the numerator and the denominator cancel. When a factor

**in the**denominator does not cancel, it produces a vertical

**asymptote**.