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

##### 1 Answer

May 15, 2017

Vertical:

Horizontal:

#### Explanation:

- Find the vertical asymptote by setting the value of the denominator(s) to zero.

#x-2=0# and therefore#x=2# . - Find the horizontal asymptote, by studying the end behavior of the function. The easiest way to do so is to use limits.
- Since the function is a composition of
#f(x)=x-2# (increasing) and#g(x)=1/x+1# (decreasing), it is decreasing for all defined values of#x# , i.e.#(-oo,2]uu[2,oo)# . graph{1/(x-2)+1 [-10, 10, -5, 5]}

*Other examples:*

What is the zeros, degree and end behavior of