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.