Question

What is the definition of asymptote?

What is the facts or characteristics of asymptote?
What is some examples of asymptote?
What is some non-examples of asymptote?

Answer 1

An asymptote is a line that approaches a curve indefinitely without intersecting it at any finite point. Examples include the line y = 0 for the function y = 1/x, whereas a non-example would be the intersecting line y = x with a parabola y = x^2.

Step-by-step explanation:

An asymptote is a line that a curve approaches as it heads towards infinity, but never actually reaches.

There are several characteristics of an asymptote that are notable. First, the distance between the curve and the asymptote approaches zero as one moves along the curve towards infinity. However, the curve will never intersect the asymptote at any finite point. There are two main types of asymptotes: vertical and horizontal.

An example of an asymptote is the line y = 0, which is a horizontal asymptote for the function y = 1/x as x approaches infinity.

A common non-example of an asymptote is any line or curve that intersects a graph at a finite number of points, such as the line y = x when compared with a parabola y = x2.

Answer 2

A straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line.