Question

Check symmetry with respect to both axes and the origin of the graph of x^2y-x^2+4y=0

Answer 1

Please help!

Answer 2

simple way is to replace x by -x and see if you get the same function
then try replacing y by -y and see if you get the same function
if thats the case it should be symm wrt to both axis or to either x if -x returns the same functin, or y if -y returns the same function

Answer 3

Thanks!

Answer 4

do you have the answers?
lets verify the work

Answer 5

Okay, thank you.
I thought I should factor out the x^2 does that make sense?

Answer 6

no, say you put x = -x then you will have
(-x)^2y-(-x)^2+4y=0
which is same as original function as (-x)^2= x^2
so symettrical to x ,
then try for -y and it is not similar to original function

Answer 7

Oh! okay, thank you. That makes sense, I thought maybe factoring would make the answer seem easier but that is what i was taught. Thank you so much!