Curriculum
Course: General Mathematics — Second Secondary
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Curriculum

General Mathematics — Second Secondary

Unit 1: Real Functions and Curve Sketching

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Unit 2: Exponents, Logarithms and Applications

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Unit 3: Limits

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Unit 4: Trigonometry

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Text lesson

Even and Odd Functions

General Mathematics — Second Secondary

Even and Odd Functions

Definition of even and odd

Definition of even and odd

  1. We test a function f by putting (−x) in place of x in its rule
  2. and
  3. comparing the result with f(x):
Comparison aspectMain ideaKeywords
Even function
  • f(−x) = f(x) for every x in the domain. The graph is symmetric about the y-axis
  • so if (a
  • b) lies on the graph then (−a
  • b) also lies on it
everydomaingraphsymmetric
Odd function
  • f(−x) = −f(x) for every x in the domain. The graph is symmetric about the origin
  • so if (a
  • b) lies on the graph then (−a
  • −b) also lies on it
everydomaingraphsymmetric
Essential condition
  • the domain must be symmetric about zero. The function f(x) = √x is neither even nor odd
  • because its domain [0
  • ∞[ is not symmetric
domainmustsymmetriczero
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