Question

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

Answer 1

Please Explain how you did it!

Answer 2

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)

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

yes

Answer 7

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?

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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.

Answer 13

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.

Answer 14

Is your question if that your work is right?

Answer 15

yea! and if the axis is correct

Answer 16

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".

Answer 17

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.

Answer 18

Heres an example.

Answer 19

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