SOLUTION: Decide whether or not the equation defines y as a function of x. {{{x-y^2=-2}}} What I got: {{{x-y^2=-2}}} {{{x=-2+y^2}}} {{{sqrt(x+2)=y}}} Is it a function?

Algebra ->  Functions -> SOLUTION: Decide whether or not the equation defines y as a function of x. {{{x-y^2=-2}}} What I got: {{{x-y^2=-2}}} {{{x=-2+y^2}}} {{{sqrt(x+2)=y}}} Is it a function?       Log On


   

Question 755537: Decide whether or not the equation defines y as a function of x.
x-y%5E2=-2
What I got:
x-y%5E2=-2
x=-2%2By%5E2
sqrt%28x%2B2%29=y
Is it a function?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
No it does not express y as a function of x. You did actually find part of the equation in the form of y as a function of x. The original equation ALSO has a lower branch which is also a function of x.

Taking square root of y%5E2=x%2B2, you have BOTH of these:
y=sqrt%28x%2B2%29 AND highlight%28y=-sqrt%28x%2B2%29%29

Consistant with that, +x-y%5E2=-2 IS NOT A FUNCTION.

A reason it is not a function is because for all but one value of x, each value of x gives more than one value of y.
graph%28300%2C300%2C-3%2C9%2C-6%2C6%2Csqrt%28x%2B2%29%2C-sqrt%28x%2B2%29%29