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)**.

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