# How do you graph #f(x)=2/(x-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 1 Answer

graph{2/(x-1) [-10, 10, -5, 5]}

X intercept: Does not exist

Y intercept: (-2)

Horizontal asymptote:0

Vertical asymptote: 1

#### Explanation:

First of all to figure the y intercept it is merely the y value when x=0

So y is equal to

Next the x intercept is x value when y=0

This is a nonsense answer showing us that there is defined answer for this intercept showing us that their is either a hole or an asymptote as this point

To find the horizontal asymptote we are looking for when x tends to

Constants to infinity are just constants

x variables to infinity are just infinity

Anything over infinity is zero

So we know there is a horizontal asymptote

Additionally we could tell from

C~ vertical asymptote

D~ horizontal asymptote

So this shows us that the horizontal asymptote is 0 and the vertical is 1.