# Symmetry in Graphs of Functions and Relations

Symmetry in Graphs of Functions and Relations

This Demonstration shows the three types of symmetry commonly studied in graphs: symmetry with respect to the axis, the axis, or the origin.

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y

A graph has symmetry with respect to the axis if reflecting it across the axis yields an identical graph. The graph of an equation has this symmetry if replacing with in the equation yields the identical equation.

x

x

y

-y

A graph has symmetry with respect to the axis if reflecting it across the axis yields an identical graph. The graph of an equation has this symmetry if replacing with in the equation yields the identical equation.

y

y

x

-x

A graph has symmetry with respect to the origin if reflecting the graph across both the axis and axis yields an identical graph. The graph of an equation has this symmetry if replacing with and with in the equation yields the identical equation.

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y

x

-x

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-y