How do you find the verticle asymptote?

Question

find it of this: (5) / (x^2 - 5x)

Answer 1

I believe a vertical asymptote will only occur at a point where you get a division by zero. I can't think of another way to get one at least. Division by zero does not guarantee a vertical asymptote though.

To find the vertcal asymptotes, you first find the places where you get a division by zero. Then you must take the limit as x approaches that value from the left and the right to see if there's actually an asymptote there. (The limit will approach negative or positive infinity).

An example of a function that doesn't have an asymptote where you divide by zero:
f(x) = (x^2 - 4)/(x - 2)

Answer 2

Vertical asymptotes occur any time the function is undefined......so you can set the denominator to zero, and solve.

x^2-5x=0
x(x-5)=0
x=0, and x-5=0


x=0 and x=5