SOLUTION: This has been stumping me for a while...can't seem to get it. Find the equations of the asymptotes for y = 1/square root of x - 1.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: This has been stumping me for a while...can't seem to get it. Find the equations of the asymptotes for y = 1/square root of x - 1.      Log On


   

Question 12894: This has been stumping me for a while...can't seem to get it. Find the equations of the asymptotes for y = 1/square root of x - 1.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F%28sqrt%28x-1%29%29? If so, then if x=1, we get sqrt%280%29 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%28sqrt%28x-1%29%29+=+1
sqrt%28x-1%29+=+1%2Fy
x-1+=+%281%2Fy%29%5E2
x-1+=+1%2Fy%5E2
x+=+1%2Fy%5E2+%2B+1

So, what value(s) of y are not allowed? Well, if y=0, then y%5E2 is also sero, and we have a division by zero again.

--> asymptote at y=0

jon.