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.
The permanent URI of this web page
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http://tobybartels.name/MATH-1150/2011FA/symmetry/.
