SOLUTION: Does y^2 = x^2 - 1 represent y as a function of x?

Question 899704: Does y^2 = x^2 - 1 represent y as a function of x?
Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!
No.

Here is why:
Let x=k, assuming k>=0.

Solve for y.
, although there is a negative branch also; two different functions, but no matter----

Now, k^2-1>=0

OR
Meaning k must not be an fraction, neither positive nor negative.

We already took k as positive or zero, so just understand .

will be a value for y.
You can also choose x=-k and then
, which is the SAME as for x=k.

This shows that y gives the same result for x=k and for x=-k.
Those are two DIFFERENT input values giving the SAME output value.
NOT a function.
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