## anonymous 5 years ago check for symmetry, y=(x)/(x^2+1) I think thats how you set it up...

1. anonymous

check that this is odd. $\frac{odd}{even}=odd$ for functions

2. anonymous

Im so confused...

3. anonymous

ok it is symmetric with respect to the origin.

4. anonymous

we can check first with numbers and then with variables.

5. anonymous

let x = 1, $y=\frac{1}{1^2+1}=\frac{1}{2}$

6. anonymous

now let x = -1 $y=\frac{-1}{(-1)^2+1}=\frac{-1}{1+1}=-\frac{1}{2}$

7. anonymous

this says go right 1, up one half, left one, down one half.

8. anonymous

since we have $(1,\frac{1}{2})$ and also $(-1,-\frac{1}{2})$

9. anonymous

Oh! I see now! Ok, one more... xy^2+10=0, what do you do with the 10?

10. anonymous

are you sure? we should check with variables as well. x = a, get $y=\frac{a}{a^2+1}$ x = -a get $y=-\frac{a}{a^2+1}$

11. anonymous

so symmetric wrt the origin.

12. anonymous

yeah i get it. the x=1 thing helped

13. anonymous

$xy^2+10=0$ $xy^2=-10$ $x=-\frac{10}{y^2}$

14. anonymous

ahhhh thank you!

15. anonymous

numbers always help

16. anonymous

system is weird ignore last remark.

17. anonymous

Well thank you very much, helps a lot1