## jewlzme17 one year ago Which Symmetry? Options: Y axis symmetry,X axis symmetry, and Origin symmetry. 1. x-y^2=0 2. y= x^4-x^2+3 3.y=x/x^2+1 4. y=(sqrt 9-x^2) 5.xy^2+10=0 6. xy=4

1. jewlzme17

Please Explain how you did it!

2. anonymous

See if this helps. ODD Functions: Opposite X's and Opposite Y's and symmetrical to the origin. EVEN Functions: Opposite X's nut Equal Y's. In that case even functioms would be symmetrical to the y axis. If you have opposite x's and opposite y's then that means you are symmetrical to the origin. Ex: (5,10) (-5,-10). With X- Axis, your Y values change. Ex: (-3,5) (-3,-5)

3. anonymous

Try and solve the first one, and ill let you know if you got it.

4. jewlzme17

okay so x-y^2=0 will go to (-x)-y^2=0 so it would be y axis symm

5. anonymous

Let me ask this first. Do you agree at x^2, it creates a parabla

6. jewlzme17

yes

7. anonymous

The equation ultimately ends up being. X=Y^2. You probabably recognize the opposite of that, Y=X^2. With Y=x^2 the parabla would make a U shape that would mean the ordered pairs would have opposite x's but equal y's or in other words, symmetrical to the y axis.. Now if X is what your trying to find, what must it be symmetrical to?

8. anonymous

Does any of that make sense to you? Do i need to clarify anything?

9. jewlzme17

yea it kind of does! ha but for the x axis you change the y. So from (x,y) to (x,-y)

10. anonymous

Yes exactly. Think of the parabola on it's side. Like how Y=x^2 the parabola went through (0,0) and the two pieces curved up on each side of the y axis. In this case, your just flipped on the x-axis, and instead of your x values changing, your y values change, exactly like you mentioned

11. jewlzme17

okay so it would be x-y^2=0 to x+y^2=0

12. anonymous

No. The question you asked, was what would be the symmetry. The symmetry would be over the x-axis. x-y^2=0 to x+y^2=0 can lead to 2 separate functions: x-y^2=0 ends up being x=y^2. x+y^2=0 ends up being x=-y^2. Making the parabola negative negates it, and flips facing the other direction.

13. jewlzme17

would 5 be xy^2+10=0 to x(-y)^2+10=0 to xy^2+10=0 so it is the x -axis? But no I know that it's just I'm showing my work on how.

14. anonymous

15. jewlzme17

yea! and if the axis is correct

16. anonymous

Your axis is correct. It is symmetrical over the x-axis. However im confused with what you typed "xy^2+10=0 to x(-y)^2+10=0 to xy^2+10=0".

17. anonymous

What I would do personally, is make a table with your x values. and just plug them in and see if they follow any particular rule.

18. anonymous

Heres an example.

19. jewlzme17

that was me changing symbols and then solving ha idk that is what my teacher taught me.

20. anonymous

|dw:1439880356001:dw|

21. anonymous

That is very sloppy but it proves my point. These numbers aren't real, its just to prove a point. If you were to plug in x=1, you would get y=2. But if you were to also plug in x=1 to the equation, you would get y=-2

22. anonymous

Do you know what applies to each symmetrical value?

23. jewlzme17

okay yea I see what you are saying! What about the other questions? like idk what to do with the whole sqrt or the fraction.

24. jewlzme17

But do you mean what it converts to?

25. anonymous

yeah

26. anonymous

i have the rules out in front of me, i can type it out if you think you may need it.

27. jewlzme17

for the x axis it changes from (x,y) to (x,-y) for the y axis it changes from (x,y) to (-x,y) and for origin it changes from (x,y) to (-x,-y)

28. anonymous

ok, lets try number 4

29. anonymous

Just clarifying this is the equation: $y=\sqrt{9}-x^2$

30. jewlzme17

the sqrt is over the whole equation

31. jewlzme17

$y=\sqrt{9-x^2}$

32. anonymous

ok, well what do you think you should do.

33. anonymous

what step would you take first.

34. jewlzme17

um changing -x^2 into a positive x^2? I don't know

35. anonymous

Not quite, y is already by itself so all you really need to do is just plug and chug. For example, say you plug in 3 or even -3 for x. you would get $y=\sqrt{9-9}$

36. anonymous

2 ordered pairs right out the bat would be, 3,0 and -3,0

37. jewlzme17

okay so it would be y axis

38. anonymous

yeah exactly, plugging in some other numbers would get you decimals. I was just too lazy.

39. jewlzme17

hahaa okay! I understand it so much better now! Thank you!

40. anonymous

No problem, glad I could help! If you need any future help, just let me know.

41. jewlzme17

I will! Thank you so much again!