## Rational functions

Reciprocal function. A function  is called a reciprocal function if

with constant value . The domain of  is , that is, the set of all real values except .

1. If , increases without bound as approaches 0 from the right, and decreases without bound as approaches 0 from the left. In short, we write

as     and     as .

2. If , decrease without bound as approaches 0 from the right, and increases without bound as approaches 0 from the left. In short, we write

as     and     as .

 1. 2.

Linear rational functions. A function  is called a linear rational function if

 (1)

Rational functions. A function  is called a rational function if

 (2)

with polynomial functions  of degree  and  of degree .

Department of Mathematics