What is an asymptote?

1 Answer
Jan 28, 2015

An asymptote is a value of a function that you can get very near to, but you can never reach.

Let's take the function #y=1/x#
graph{1/x [-10, 10, -5, 5]}
You will see, that the larger we make #x# the closer #y# will be to #0#
but it will never be #0# #(x->oo)#

In this case we call the line #y=0# (the x-axis) an asymptote

On the other hand, #x# cannot be #0# (you can't divide by#0#)

So the line #x=0# (the y-axis) is another asymptote.