How do you find the vertical, horizontal and slant asymptotes of: #(x-3)/(x-2)#?

1 Answer
Jun 6, 2016

Answer:

Use the fact that #(x-3)/(x-2) = (x-2-1)/(x-2) = (x-2)/(x-2) - 1/(x-2) = 1 - 1/(x-2)#.

Explanation:

I suppose you meant oblique asymptote, which intuitively refers to the 'slant' asymptote.

To find asymptotes, we check the #x# and #y# values where the function is undefined.

When #x-2=0#, the function is undefined. Thus the vertical asymptote is #x=2#.

Also, notice that as #x# gets larger, #1/(x-2)# gets smaller, but never zero. Thus, the function will never take on the value #y=1#, and thus that is the vertical asymptote.