SOLUTION: Given y=x/(x^2+1), use the algebraic tests to determine symmetry with respect to both axes and the origin.
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Question 267380: Given y=x/(x^2+1), use the algebraic tests to determine symmetry with respect to both axes and the origin. Answer by drk(1908) (Show Source):
You can put this solution on YOUR website! To be symmetric to the x axis replace y with -y. we get
-y=x/(x^2+1)
which is
y=-x/(x^2+1)
or
f(x) - - - > -f(x)
therefore, not symmetric to the x axis
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To be symmetric to the y axis replace x with -x. we get
y = -x/(x^2+1)
or
f(x) - - -> -f(x)
therefore, not symmetric to the x axis
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To be symmetric to the origin replace x with -x AND y with -y. we get
-y=-x/(x^2+1)
which is
y=x/(x^2+1)
f(x) - - - -> f(x)
Therefore, symmetric to origin.
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here is the graph.
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