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WOLFRAM|DEMONSTRATIONS PROJECT

Symmetry in Graphs of Functions and Relations

​
equation
y=
2
x
+3x
symmetry check
none
x axis
y axis
origin
list types of symmetry?
types of symmetry: none
This Demonstration shows the three types of symmetry commonly studied in graphs: symmetry with respect to the
x
axis, the
y
axis, or the origin.
A graph has symmetry with respect to the
x
axis if reflecting it across the
x
axis yields an identical graph. The graph of an equation has this symmetry if replacing
y
with
-y
in the equation yields the identical equation.
A graph has symmetry with respect to the
y
axis if reflecting it across the
y
axis yields an identical graph. The graph of an equation has this symmetry if replacing
x
with
-x
in the equation yields the identical equation.
A graph has symmetry with respect to the origin if reflecting the graph across both the
x
axis and
y
axis yields an identical graph. The graph of an equation has this symmetry if replacing
x
with
-x
and
y
with
-y
in the equation yields the identical equation.
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