Question 267380
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.
{{{ graph( 300, 200, -10, 10, -10, 10, x/(x^2+1)) }}}