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IB DP Maths: AA HL復習筆記2.3.3 Symmetry of Functions

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月11日 下午6:37

What are odd functions?

What are even functions?

What are the symmetries of graphs of odd & even functions?

  • The graph of an?odd?function has?rotational symmetry
    • The graph is unchanged by a?180° rotation?about the origin
  • The graph of an?even?function has?reflective symmetry
    • The graph is unchanged by a?reflection?in the?-y-axis

Exam Tip

  • Turn your GDC upside down for a quick visual check for an odd function!
    • Ignoring axes, etc, if the graph looks exactly the same both ways, it's odd

Worked Example

2-3-3-ib-aa--ai-we-image-a

2-3-3-ib-aa-hl-odd-even-functions-a-we-solution

2-3-3-ib-aa-hl-odd-even-functions-b-we-solution

 

Periodic Functions

What are periodic functions?

  • What are the symmetries of graphs of periodic functions?
  • The graph of a?periodic?function has?translational symmetry
    • The means that the graph appears to?repeat?the same section (cycle) infinitely

Exam Tip

  • Worked Example

2-3-3-ib-aa--ai-we-image-c

2-3-3-ib-aa-hl-periodic-functions-we-solution

 

Self-Inverse Functions

What are self-inverse functions?

What are the symmetries of graphs of self-inverse functions?

  • The graph of a?self-inverse?function has?reflective symmetry
    • The graph is unchanged by a?reflection?in the line?y?=?x

Exam Tip

Worked Example

2-3-3-ib-aa-hl-self-inverse-functions-we-solution

 

 

 

 

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