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)**

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