what is the meaning of asymptote?

Question

can you please explain it in a simplified way?

Answer 1

An asymptote is some type of imaginary line on a graph that serves as a boundary that a function approaches, but never actually touches.

Imagine, for example, the function y = (1/x). In this function, The line x = 0 (which is the y-axis) is the asymptote of the function, as division by zero is impossible. But, you can plug the values 1, 0.1, 0.01, 0.001,...to infinitesmally small numbers. But no matter what, the function is undefined at that point. (1/x) will always approach, but never touch, the line x = 0.

Answer 2

Here is a definition which might help you: A straight line that a curve approaches but never meets or crosses. The curve is said to meet the asymptote at infinity. In the equation y = 1/x, y becomes infinitely small as x increases but never reaches zero.

For example in the graph y = 1/x the curve of the graph will approach the line x = 0 and y = 0. The lines x = 0 and y = 0 are the asymptotes of the equation.

As the value of x gets larger y will get smaller and smaller approaching 0, but never get there. This is because x could be infinitely large.

Have a good think about it. That how it became clear to me.

Answer 3

I think the first answer is a good one. However, I want to point out that sometimes a graph can cross the asymptote once, and then proceed to approach it without crossing. For instance, look at the graph:

f(x) = (x) / (x^2 -1)

This graph has as an asymptote the line y=0. However, there is one point on the graph, (0,0), that is actually on the asymptote.

In general though, an asymptote is an imaginary line that a graph eventually approaches without crossing or touching.

Hope this helps.

Answer 4

Look at 1/(x-3).
If x=3+p while p is very very small positive number
then 1/((x-3) =1/p and that is very much
Example: if p=a millionth, then 1/(x-3) = a million.
If p=a billionth, then 1/(x-3) = a billion.
The smaller p, the more is 1/(x-3)
If x is going down to 3
1/(x-3) tends to infinity.
The vertical line x=3 is the asymptote of the graph of 1/(x-3).
It looks like a tangent, but it is not, because x=3 exactly has not been allowed. You may not divide by 0.

Answer 5

An asymptote is a straight line or curve A to which another curve B (the one being studied) approaches closer and closer as one moves along it. As one moves along B, the space between it and the asymptote A becomes smaller and smaller, and can in fact be made as small as one could wish by going far enough along. A curve may or may not touch or cross its asymptote. In fact, the curve may intersect the asymptote an infinite number of times.

If a curve C has the curve L as an asymptote, one says that C is asymptotic to L.

Answer 6

No, no, no - an asymptote to a curve is a straight line that the curve approaches. It *can* touch it, even infinitely many times - for instance, sinx/x has y = 0 as an asymptote. It also is not necessary for x to go to infinity. 1/(1 - x) has an asymptote at y = 1.

Answer 7

An asymptote (of a curve) is that line to which this curve slowly tends to merge as the x-axis value keeps changing, but never touches it.

So, if you were to plot 1/x, for x becoming increasingly small and smaller, you would observe that 1/x keeps on increasing and the graph will almost be touching y axis, but that will never happen (as touching y-axis implies x=0, and at x=0, the value of 1/x is undefined)

The line x=0 is the asymptote of the curve, y=1/x.

Answer 8

A straight line that a curve approaches but never meets or crosses. The curve is said to meet the asymptote at infinity. In the equation y = 1/x, y becomes infinitely small as x increases but never reaches zero

Answer 9

No, it just means a vertical tangent. This doesn't have to include an asymptote. For example, if you consider a semicircle, the edges of the semicircle have a infinite gradient (since their tangents are vertical), but are not asymptotes.

Answer 10

it's more likely to use in graph, it's a invisble line to set the limitation, no mater when, the line wont pass to the asymptote.
not all the graph has asymptote.