What are the asymptotes for #1/x#?

1 Answer
Oct 17, 2015

Answer:

Have a look:

Explanation:

Here, for your function #y=1/x#, you have 2 types of asymptotes:

1) Vertical:
This is obtained looking at the point(s) of discontinuity of your function. These are problematic points where, basically, you cannot evaluate your function. In your case the point of coordinate #x=0# is one of these type of points. If you try using #x=0# into your function you get #y=1/0# which cannot be evaluated.
So the vertical line of equation #x=0#, the #y# axis, will be your VERTICAL ASYMPTOTE.

2) Horizontal.
This is a little bit more tricky...
You need to find a horizontal line towards which your function tends to get closer and closer.
One way to find this is to "see" what happens when #x# tends to become very big positively or negatively, i.e., #x->+-oo#.
You can see that, for #y=1/x#, when #x# becomes very big then #y# becomes very small....or tends to zero, #y->0#!!!
Basically, the #x# axis is your HORIZONTAL ASYMPTOTE!!!!

You can see these two asymptote graphically as the two lines near which the curve (representing your function) tends to get near to:
graph{1/x [-10, 10, -5, 5]}