Symmetry and intercepts (§2.2)
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 between 2010 and 2012 by Toby Bartels,
last edited on 2012 March 30.
Toby reserves no legal rights to it.
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