## Transformations of Graphs

There are many ways that graphs can be transformed but many of them can be expressed as– transformations,– transformations, an– transformation followed by a– transformation or vice versa. The transformations together with their effects are summarised below.

is transformed to | or- transformation or both | Effect |

Scaling byin the- direction | ||

Scaling by 3 in the- direction | ||

Scaling by 4 in the- direction | ||

Translation in the +ve- direction by 2 | ||

Translation in the -ve- direction by 1 | ||

The left hand side or -ve- part of the graph disappears and is replaced by the reflection of the right hand side of the graph reflected in the y - axis. | ||

The -vepart of the graph is reflected in the- axis | ||

Translation in the -ve- direction by 3 | ||

Translation in the +ve– direction by 1 | ||

Scaling in the– direction by | ||

both | Translation in the +ve– direction by 1 and scaling in the– direction by 2 | |

both | Scaling in the– direction byand translation in the- direction by -1 | |

both | Translation in the -ve- direction by 1 and in the -ve– direction by 2 |

Summary of Transformations

You must first decide for each transformation whether it is anor – transformation. Thetransformations are always counter intuitive:means move 2 in the negative– direction andmeans scale byin the– direction.