What are the asymptotes of $y=1/(x-2)$ and how do you graph the function?

Question

8605 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-23T12:47:50

Vertical asymptote: $x=2$ and horizontal asymptote: $y=0$
Graph - Rectangular hyperbola as below.

$y = 1/(x-2)$

$y$ is defined for $x in (-oo,2) uu (2,+oo)$

Consider $lim_(x->2^+) y =+oo$

And $lim_(x->2^-) y =-oo$

Hence, $y$ has a vertical asymptote $x=2$

Now, consider $lim_(x->oo) y =0$

Hence, $y$ has a horizontal asymptote $y=0$

$y$ is a rectangular hyperbola with the graph below.

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

What are the asymptotes of y=1/(x-2)y=1/(x-2) and how do you graph the function?