Function Properties (HSC SSCE Mathematics Advanced): Flashcards

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Even and Odd Functions
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Algebraic condition for even function

f(x)=f(x)f(-x) = f(x) for all xx in domain

Algebraic condition for odd function

f(x)=f(x)f(-x) = -f(x) for all xx in domain

Type of symmetry for even functions

Reflective symmetry about the yy-axis

Type of symmetry for odd functions

180° rotational symmetry about the origin

Classification of f(x)=x2f(x) = x^2

Even function

Classification of f(x)=x3f(x) = x^3

Odd function

First step to test function symmetry

Substitute x-x into the function

Function type if f(x)=f(x)f(-x) = f(x)

Even

Function type if f(x)=f(x)f(-x) = -f(x)

Odd

Functions satisfying neither symmetry condition

Neither even nor odd

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