Question 12894
an asymptote occurs where there is no value allowable. This typically occurs when you have a fractional equation. Here, you need to figure out what value(s) of the variable make the denominator zero, as anything divided by zero gives an error.


i assume you mean {{{y = 1/(sqrt(x-1))}}}? If so, then if x=1, we get {{{sqrt(0)}}} on the denominator, which is zero... division by zero is not allowed, so:


--> aymptote at x=1.


Now how about any y-values not allowed? Well, just rearrange the equation as follows:


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


So, what value(s) of y are not allowed? Well, if y=0, then {{{y^2}}} is also sero, and we have a division by zero again.


--> asymptote at y=0


jon.