# Graphs: symmetry and intercepts

The pattern here is that you always mess with the *other* variable.
## Symmetry

You can test symmetry using either the equation or the graph.
- Symmetry with respect to the
*x*-axis:
- change
*y* to −*y* in the equation,
and see if this is equivalent to the original equation;
- change each point (
*x*, *y*) on the graph
to (*x*, −*y*),
and see if this is also a point on the graph.
- Symmetry with respect to the
*y*-axis:
- change
*x* to −*x* in the equation,
and see if this is equivalent to the original equation;
- change each point (
*x*, *y*) on the graph
to (−*x*, *y*),
and see if this is also a point on the graph.
- Symmetry with respect to the origin:
- change both
*x* to −*x* and *y* to −*y*
in the equation,
and see if this is equivalent to the original equation;
- change each point (
*x*, *y*) on the graph
to (−*x*, −*y*),
and see if this is also a point on the graph.

Each kind of symmetry is a separate Yes/No question.
## Intercepts

An intercept is a point on a graph that is also on one of the axes.
*x*-intercepts:
- in the equation, set
*y* to 0 and solve for *x*;
- any point (
*x*, 0) on the graph is an *x*-intercept.
*y*-intercepts:
- in the equation, set
*x* to 0 and solve for *y*;
- any point (0,
*y*) on the graph
is a *y*-intercept.

Every intercept is a point with two coordinates.

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This web page was written in 2010 and 2011 by Toby Bartels,
last edited on 2011 April 5.
Toby reserves no legal rights to it.
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