IB DP Maths: AA HL复习笔记2.3.3 Symmetry of Functions
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
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
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
转载自savemyexams
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