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Question 995537: True or False
The rule y^2 = x^3 defines a function.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i would say false.
y^2 = x^3 is solved as follows:
take the square root of both sides to get:
y = plus or minus sqrt(x^3)
that plus or minus tell you that you have more than one value of y for each value of x.
for example:
assume that x = 4.
you have y^2 = x^3 which means that y^2 = 64 when x is 4 because 4^3 = 64.
take the square root of both sides of that equation to get y = +/- 8.
for the value of x = 4, you can get y = + 8 or - 8.
more than one value of y for a given value of x means that you do not have a function since that violates the rules of a function that state that there is one and only one value of y for each and every value of x.
there may be only one possible value of y^2, but there are more than one possible value of y.
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