SOLUTION: Determine whether the equation is a function. x^2-4y^2=1

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Question 674461: Determine whether the equation is a function.
x^2-4y^2=1
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine whether the equation is a function.
x^2-4y^2=1
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It is not a function because there are 2 y-values for each
x value.
4y^2 = x^2-1
y^2 = (x^2-1)/4
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y = +Sqrt[(x^2-1)/4] AND = -sqrt[(x^2-1)/4]
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Cheers,
Stan H.
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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-4y%5E2=1

graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2-4y%5E2%3E=1+%29


so, your equation is hyperbola
the "basic" hyperbola y=1%2Fx is the function, but not all hyperbolas are functions:


+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+1%2Fx%29+

the ones that are NOT functions are in the form of x%5E2%2Fa%5E2+-+y%5E2%2Fb%5E2+=+1; whenever y is squared, you do not+have a functions
so, your hyperbola is not a function