Curriculum
Pure Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
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Unit 2: Exponents and Logarithms
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Unit 3: Limits
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Unit 4: Trigonometry
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Text lesson
Properties of Functions
Properties of Functions
Even and odd functions
Even and odd functions
- We test a function by replacing x with (−x) in its rule
- then comparing the result with the original function f(x):
Key points
Even functionf(−x) = f(x) for every x in the domain. Its graph is symmetric about the y-axis, for example f(x) = x².
Odd functionf(−x) = −f(x) for every x in the domain. Its graph is symmetric about the origin (0, 0), for example f(x) = x³.
Neitherif neither condition holds for all x in the domain.
The domain must be symmetric about zeroif x belongs to the domain, then −x must also belong to it. Otherwise the function cannot be even or odd.
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