How do horizontal and vertical transformations affect each other?
Horizontal and vertical transformations are independent of each other
The horizontal transformations involved will need to be applied in their correct order
The vertical transformations involved will need to be applied in their correct order
Suppose there are two horizontal transformation H1 then H2 and two vertical transformations V1 then V2thenthey can be applied in the following orders:
Horizontal then vertical:
H1 H2 V1 V2
Vertical then horizontal:
V1 V2 H1 H2
Mixed up (provided that H1 comes before H2 and V1 comes before V2):
H1 V1 H2 V2
H1 V1 V2 H2
V1 H1 V2 H2
V1H1 H2V2
Exam Tip
In an exam you are more likely to get the correct solution if you deal with one transformation at a time and sketch the graph after each transformation
Worked Example
Composite Vertical Transformations af(x)+b
How do I deal with multiple vertical transformations?
Order matters when you have more than one vertical transformations
If you are asked to find the equation then build up the equation by looking at the transformations in order
Worked Example
Composite Horizontal Transformations f(ax+b)
How do I deal with multiple horizontal transformations?