Rational Functions

The criterion is given by a quotient between polynomials:

Rational Functions

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

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

Also, hyperbolas are the graphs of the functions Hyperbola.

The simplest hyperbola is represented with the equation Hipérbola  .

Its asymptotes are the axes.

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

Hyperbola

Hyperbola Graph

1. Vertical Translation

Vertical Translation

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

If a>0, Hyperbola moves upward a units.

Hyperbola

Vertical Translation

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

If a<0, Hyperbola moves down a units.

Hyperbola

Vertical Translation

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


2. Horizontal Translation

Vertical Translation

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

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

Hyperbola

Horizontal Translation

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

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

Hyperbola

Horizontal Translation

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

3. Oblique Translation

Hyperbola

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

Hyperbola

Oblique Translation

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

To graph hyperbolas of the type:

Hyperbola

It is divided and is written as:

Hyperbola

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

Hyperbola

Hyperbola Operations

Hyperbola

Oblique Translation

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