The graphs given by the equationare called hyperbolae. One is illustrated below.

In fact there are a set of equations which all give the same shape of graph as shown above. The graphs may be moved up or down, translated, rotated or any combination of these, but the shapes of the graphs are still fundamentally the same. The rules of transformation are just the normal transformation of graph rules. For simple transformations like these, it does not matter whether you applyor– transformations first.

– transformations |
– transformations |

Translate the graph left 3. |
Translate the graph up 2. |

Scale the graph by a factor 3 in thedirection. |
Scale the graph by a factor 2 in thedirection. |

Reflect the graph in the– axis |
Reflect the graph in the– axis. |

Example: Sketch the graph

There are two transformations: a translation 3 in the– direction and a scaling by 2 in the– direction. The graph is sketched below.