# Rational Functions

The criterion is given by a quotient between polynomials:

The domain is equal to , minus the values of x that would annul the denominator.

The functions of the type has a hyperbola in its graph.

Also, hyperbolas are the graphs of the functions .

The simplest hyperbola is represented with the equation  .

Its asymptotes are the axes.

The center of the hyperbola, which is where the asymptotes intersect, is the origin.

#### 1. Vertical Translation

The center of the hyperbola is (0, a).

If a>0, moves upward a units.

The center of the hyperbola is: (0, 3)

If a<0, moves down a units.

The center of the hyperbola is: (0, −3)

#### 2. Horizontal Translation

The center of the hyperbola is: (−b, 0).

If b> 0, is shifted to the left b units.

The center of the hyperbola is: (−3, 0)

If b<0, is shifted to the right b units.

The center of the hyperbola is: (3, 0)

#### 3. Oblique Translation

The center of the hyperbola is: (−b, a).

The center of the hyperbola is: (3, 4).

To graph hyperbolas of the type:

It is divided and is written as:

Its graph is a hyperbola with a center (−b, a) and asymptotes parallel to the axes.

The center of the hyperbola is: (−1, 3).