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

1 Answer
Rohan N.
Apr 22, 2018

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

y=2/(0-1)

y=2/-1=-2

So y is equal to -2 so we get the co-ordinate pair (0,-2)

Next the x intercept is x value when y=0

0=2/(x-1)

0(x-1)=2/

0=2

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 oo or -oo

lim x to oo 2/(x-1)

(lim x to oo2)/(lim x to oox- lim x to oo1)

Constants to infinity are just constants

2/(lim x to oox-1)

x variables to infinity are just infinity

2/(oo-1)=2/oo=0

Anything over infinity is zero

So we know there is a horizontal asymptote

Additionally we could tell from 1/(x-C)+D that

C~ vertical asymptote
D~ horizontal asymptote

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

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