IB DP Maths: AA HL复习笔记2.6.4 Composite Transformations of Graphs
What transformations do I need to know?
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 V2 then they 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
- V1 H1 H2 V2
- Horizontal then vertical:
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?
- Order matters when you have more than one horizontal transformations
- If you are asked to find the equation then build up the equation by looking at the transformations in order
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If a is negative then the reflection and stretch can be done in any order
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Worked Example
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