anonymous
  • anonymous
for which of these equations is y a function of x? y=3x^3 xy=1 y^2=x y^3=8x
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I'm not really sure how to answer this. Any of these y could be a function of x except the x = y^2 one because there's 2 possible outputs for the same input.
anonymous
  • anonymous
k thanks
anonymous
  • anonymous
Y is a function of x if for e given x there is only one corresponding y. y=3x^3 is OK xy=1 => y=1/x is OK y^2=x => \[y = \sqrt{x}\] is OK y^3=8x =>\[y = \sqrt[3]{8x}\] is OK You can graph these functions and when you draw a vertical line from any x value the line should intersect the graph in only one point. (only one y value for each x)

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anonymous
  • anonymous
\(y^2 = x \implies y = \pm \sqrt{x} \) Therefore it is not a function because for any one value for x, you have 2 possible values for y.
anonymous
  • anonymous
My mistake it is a function for x\[X \ge 0\]
anonymous
  • anonymous
Ok one more try it is a function if the function range is \[Y \ge 0\]

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