Help w/ symmetry prob?

Question

can someone help me with this problem b/c i don't understand what its asking to do

test for the symmetry w/ respect to both axies n origins:

1.) xy=4

2.) y=x/(x^2 +1)

thank u

Answer 1

symmetry wrt x-axis

replace y by -y .. . . and you should return to the original expression

symmetry wrt y-axis

replace x by -x .. . . and still get the original expression

symmetry wrt origin

replace y by -y and x by -x at the same time ... and return to the original expression

it turns out... they are not symmetric wrt x or y axes

but symmetric wrt origin.

.. . .. .