What are the asymptotes for 1/x?

Oct 17, 2015

Have a look:

Explanation:

Here, for your function $y = \frac{1}{x}$, 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 $y = \frac{1}{0}$ 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., $x \to \pm \infty$.
You can see that, for $y = \frac{1}{x}$, when $x$ becomes very big then $y$ becomes very small....or tends to zero, $y \to 0$!!!
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]}