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

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

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

Solve for y.
y=sqrt%28x%5E2-1%29, although there is a negative branch also; two different functions, but no matter----

Now, k^2-1>=0
k%5E2%3E=1
k%3E=1 OR k%3C=-1
Meaning k must not be an fraction, neither positive nor negative.

We already took k as positive or zero, so just understand k%3E=1.

highlight_green%28y=sqrt%28k%5E2-1%29%29 will be a value for y.
You can also choose x=-k and then y=sqrt%28%28-k%29%5E2-1%29
highlight_green%28y=sqrt%28k%5E2-1%29%29, 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.