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

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

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