Question 78017
In order to determine if this is a function lets solve for y. 


{{{x^2=1+y^2}}}


{{{x^2-1=y^2}}} Subtract 1 from both sides


{{{sqrt(x^2-1)=sqrt(y^2)}}} Take the square root of both sides

So we have


{{{y=0+-sqrt(x^2-1)}}}

Now lets graph {{{y=0+-sqrt(x^2-1)}}}. This can be broken up as

{{{y=sqrt(x^2-1)}}} or {{{y=-sqrt(x^2-1)}}}


{{{ graph( 300, 200, -6, 5, -10, 10,sqrt(x^2-1), -sqrt(x^2-1)) }}} graph of {{{y=sqrt(x^2-1)}}} and {{{y=-sqrt(x^2-1)}}}

Since the graph fails the vertical line test, it is not a function.