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).
