Testing For Symmetry and Even/Odd FunctionsDate: 06/08/98 at 20:33:45 From: Joshua Stevens Subject: Tests for symmetry and even/odd functions I'm trying to do my summer Calculus review and I cannot remember the tests for the following: -- symmetry on the x-axis -- symmetry on the y-axis -- symmetry at the origin -- even functions -- odd functions I know they are simple tests, but I just cannot remember them, nor can I find them anywhere. Thanks! Date: 06/08/98 at 23:12:09 From: Doctor Pat Subject: Re: Tests for symmetry and even/odd functions Joshua, Here are my approaches to these ideas: For symmetry on the x-axis If you replace y in the equation with -y and it is the same equation (when simplified), then it is symmetric around the x-axis. For every point (x,y) there must also be a point (x,-y). Fold the graph along the x-axis and the top and bottom match. For symmetry on the y-axis If you replace x in the equation with -x and it is the same equation (when simplified), then it is symmetric about the y-axis. For every point (x,y) there must be a point (-x,y). Fold along the y-axis and the left and right sides match. For symmetry at the origin If you replace both x and y with their negatives and it is the same equation (simplified), then it is symmetric about the origin. For every point (x,y) there is a point (-x,-y). Rotate the graph 180 degrees and the picture is the same. For even functions The process is same as symmetry in the y-axis. For odd functions The process is the same as symmetry at the origin. These names are easy to remember if you graph y= x^a. If a is odd, the graph is symmetric in the origin, if a is even the graph is symmetric in the y-axis. Hope that helps. -Doctor Pat, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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