Odd & even functions
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Flip to reveal answersDefinition of an even function?
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All 8 Flashcards — Odd & even functions
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Question
Definition of an even function?
Answer
f(−x) = f(x) — symmetric in the y-axis (e.g. x², cos x).
Question
Definition of an odd function?
Answer
f(−x) = −f(x) — symmetric about the origin (e.g. x³, sin x).
Question
How do you classify a function as odd/even?
Answer
Compute f(−x): if it equals f(x) it's even; if it equals −f(x) it's odd; otherwise neither.
Question
Integral of an odd function over [−a, a]?
Answer
0 — the halves cancel.
Question
Integral of an even function over [−a, a]?
Answer
2 × ∫₀ᵃ f(x) dx.
Question
Is x³ − 4x odd, even or neither?
Answer
Odd: f(−x) = −x³ + 4x = −(x³ − 4x) = −f(x).
Question
Which powers appear in an even polynomial?
Answer
Only even powers (and a constant); odd polynomials have only odd powers.
Question
Which function is both odd and even?
Answer
Only f(x) = 0.
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Full study notes for Odd & even functions
Topic 2.14 hub
Odd, even & self-inverse (HL only)
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