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

1 Answer
May 15, 2017

Vertical: x=2
Horizontal: y=1

Explanation:

  1. Find the vertical asymptote by setting the value of the denominator(s) to zero.
    x-2=0 and therefore x=2.
  2. Find the horizontal asymptote, by studying the end behavior of the function. The easiest way to do so is to use limits.
  3. 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]}

lim_(x->oo)1/(x-2)+1=0+1=1
Other examples:
What is the zeros, degree and end behavior of y=-2x(x-1)(x+5)?