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IB DP Maths: AA HL复习笔记2.6.4 Composite Transformations of Graphs

Category: IB课程, 教材笔记, 福利干货 Date: 2022年7月12日 上午11:09

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

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

we-image

 

2-5-4-ib-aa-sl-comp-transformation-a-we-solution

 

 

 

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

2-5-4-ib-aa-sl-comp-transformation-b-we-solution

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
      • If?a?is negative then the?reflection and stretch?can be?done in any order

Worked Example

2-6-4-ib-aa--ai-hl-comp-horizontal-trans-we-solution

 

 

 

 

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