Why are these graphs so different? y^2=x y=sqrt(x)

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Why are the graphs of y2=x and y=√x so different? They're supposed to be the same, aren't they? I'm usually good at maths but I honestly don't understand this. Can someone explain please? Thanks :).
 

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  • #2
798
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They are not different.
But do not forget the sign (+or-) in front of the square root.
And you have to plot x=y², not y=x². Since your drawing tool draws the ordinate as a function of the abscissa and that you have to plot x as a function of y (not y as a function of x as usual), you have to rotate the sheet of paper (the axes) of 90°
 

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They are not different.
But do not forget the sign (+or-) in front of the square root.
And you have to plot x=y², not y=x². Since your drawing tool draws the ordinate as a function of the abscissa and that you have to plot x as a function of y (not y as a function of x as usual), you have to rotate the sheet of paper (the axes) of 90°
Thankyou!! They are different, but your comment helped me understand why :). The y=√x is only the positive side, but when you simplify the x=y2, expression you have to add the ± to the square root. Thanks again.
 

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  • #4
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They are not different.
But do not forget the sign (+or-) in front of the square root.
And you have to plot x=y², not y=x². Since your drawing tool draws the ordinate as a function of the abscissa and that you have to plot x as a function of y (not y as a function of x as usual), you have to rotate the sheet of paper (the axes) of 90°
Call me a pedant, but generally you shouldn't "rotate the graph" - you should "reflect the graph" in the line y=x. In this particular case it happens to produce the same result. :cool:
 
  • #5
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Why are the graphs of y2=x and y=√x so different? They're supposed to be the same, aren't they? I'm usually good at maths but I honestly don't understand this. Can someone explain please? Thanks :).
They are not different.
The two graphs ARE different. The graph of y =√x is the upper half of the graph of y2 = x
But do not forget the sign (+or-) in front of the square root.
And you have to plot x=y², not y=x². Since your drawing tool draws the ordinate as a function of the abscissa and that you have to plot x as a function of y (not y as a function of x as usual), you have to rotate the sheet of paper (the axes) of 90°
 
  • #6
798
34
Hi !
The figure in my preceeding post was there in order to explain what I mean, better than with words.
Noahsdev said that he understood it.
All's well that ends well.
 

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