Even / Odd Function Checker

Enter Function

f(x) =

Use: x^2, sin(x), cos(x), sqrt(x), abs(x), log(x), exp(x), PI

Examples

Result

Enter a function above and press Check Even / Odd to see the verdict and test values.

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Condition Check

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Numerical Test Values

x	f(x)	f(−x)	f(−x) = f(x)?	f(−x) = −f(x)?

Even Functions — Y-Axis Symmetry

f(−x) = f(x) for all x in domain

A function is even if substituting −x gives exactly the same output. Graphically, the curve is a mirror image across the y-axis — fold the graph along the y-axis and the two halves match perfectly.

Common even functions:

f(x) = x² (and any even power: x⁴, x⁶, …)
f(x) = cos(x)
f(x) = |x|
f(x) = x⁴ − 3x² + 1

Shortcut: a polynomial is even if every term has an even exponent (including the constant term, exponent 0).

Odd Functions — Origin Symmetry

f(−x) = −f(x) for all x in domain

A function is odd if substituting −x gives the negative of the original output. Graphically, the curve has 180° rotational symmetry about the origin — rotating the graph half a turn leaves it unchanged.

Common odd functions:

f(x) = x (and any odd power: x³, x⁵, …)
f(x) = sin(x)
f(x) = tan(x)
f(x) = x³ − 2x

Shortcut: a polynomial is odd if every term has an odd exponent AND there is no constant term.

Still unsure about even & odd functions?