jewlzme17
  • jewlzme17
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
jewlzme17
  • jewlzme17
Please Explain how you did it!
anonymous
  • 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
  • anonymous
Try and solve the first one, and ill let you know if you got it.

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jewlzme17
  • jewlzme17
okay so x-y^2=0 will go to (-x)-y^2=0 so it would be y axis symm
anonymous
  • anonymous
Let me ask this first. Do you agree at x^2, it creates a parabla
jewlzme17
  • jewlzme17
yes
anonymous
  • 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
  • anonymous
Does any of that make sense to you? Do i need to clarify anything?
jewlzme17
  • jewlzme17
yea it kind of does! ha but for the x axis you change the y. So from (x,y) to (x,-y)
anonymous
  • 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
  • jewlzme17
okay so it would be x-y^2=0 to x+y^2=0
anonymous
  • 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
  • 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
  • anonymous
Is your question if that your work is right?
jewlzme17
  • jewlzme17
yea! and if the axis is correct
anonymous
  • 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
  • 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
  • anonymous
Heres an example.
jewlzme17
  • jewlzme17
that was me changing symbols and then solving ha idk that is what my teacher taught me.
anonymous
  • anonymous
|dw:1439880356001:dw|
anonymous
  • 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
  • anonymous
Do you know what applies to each symmetrical value?
jewlzme17
  • 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
  • jewlzme17
But do you mean what it converts to?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
i have the rules out in front of me, i can type it out if you think you may need it.
jewlzme17
  • 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
  • anonymous
ok, lets try number 4
anonymous
  • anonymous
Just clarifying this is the equation: \[y=\sqrt{9}-x^2\]
jewlzme17
  • jewlzme17
the sqrt is over the whole equation
jewlzme17
  • jewlzme17
\[y=\sqrt{9-x^2}\]
anonymous
  • anonymous
ok, well what do you think you should do.
anonymous
  • anonymous
what step would you take first.
jewlzme17
  • jewlzme17
um changing -x^2 into a positive x^2? I don't know
anonymous
  • 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
  • anonymous
2 ordered pairs right out the bat would be, 3,0 and -3,0
jewlzme17
  • jewlzme17
okay so it would be y axis
anonymous
  • anonymous
yeah exactly, plugging in some other numbers would get you decimals. I was just too lazy.
jewlzme17
  • jewlzme17
hahaa okay! I understand it so much better now! Thank you!
anonymous
  • anonymous
No problem, glad I could help! If you need any future help, just let me know.
jewlzme17
  • jewlzme17
I will! Thank you so much again!

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