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

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- jewlzme17

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- jewlzme17

Please Explain how you did it!

- 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)

- anonymous

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

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## More answers

- jewlzme17

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

- anonymous

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

- jewlzme17

yes

- 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?

- anonymous

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

- jewlzme17

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

- 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

- jewlzme17

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

- 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.

- 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.

- anonymous

Is your question if that your work is right?

- jewlzme17

yea! and if the axis is correct

- 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".

- 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.

- anonymous

Heres an example.

- jewlzme17

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

- anonymous

|dw:1439880356001:dw|

- 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

- anonymous

Do you know what applies to each symmetrical value?

- 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.

- jewlzme17

But do you mean what it converts to?

- anonymous

yeah

- anonymous

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

- 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)

- anonymous

ok, lets try number 4

- anonymous

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

- jewlzme17

the sqrt is over the whole equation

- jewlzme17

\[y=\sqrt{9-x^2}\]

- anonymous

ok, well what do you think you should do.

- anonymous

what step would you take first.

- jewlzme17

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

- 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 \[y=\sqrt{9-9}\]

- anonymous

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

- jewlzme17

okay so it would be y axis

- anonymous

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

- jewlzme17

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

- anonymous

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

- jewlzme17

I will! Thank you so much again!

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