# Graphs: symmetry and intercepts

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

A graph is **symmetric** (in a certain way)
if, when you change the points on the graph (in a certain way),
you get back the same graph.
If you have an equation for the graph,
then you can change the variables in the equation
and see if you get back the same equation.
- Symmetry with respect to the
*x*-axis:
- change
*y* to −*y*;
- Symmetry with respect to the
*y*-axis:
- change
*x* to −*x*;
- Symmetry with respect to the origin:
- change both.

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

An **intercept** of a graph
is a point on the graph that is also on one of the axes.
If you have an equation for the graph,
you can find one kind of intercept by setting the other variable to zero.
*x*-intercept:- set
*y* to 0;
*y*-intercept:- set
*x* to 0.

Every intercept is a point with two coordinates.

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This web page was written in 2010 by Toby Bartels,
last edited on 2010 October 11.
Toby reserves no legal rights to it.
The permanent URI of this web page
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`http://tobybartels.name/MATH-1150/2010FA/symmetry/`

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