# How do you describe the asymptote of a graph?

## How do you describe the asymptote of a graph?

An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.

What are asymptotes give examples?

The asymptote (s) of a curve can be obtained by taking the limit of a value where the function does not get a definition or is not defined. An example would be \infty∞ and -\infty −∞ or the point where the denominator of a rational function is zero.

### What is a curved asymptote?

In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.

What are the three types of asymptote?

An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique. That is, as approaches from either the positive or negative side, the function approaches positive or negative infinity.

#### How do you define a horizontal asymptote?

The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.

• Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0.
• Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote.

What is a curvilinear asymptote?

A curvilinear asymptote is an asymptote that’s a curve. As x approaches ∞ (or -∞), the function will approach the curve. For example, we could have a function that gets closer to the parabola y = x2 as x approaches ∞ or -∞: © 2022 Shmoop University.

## How do you identify an asymptote?

The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.

1. Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0.
2. Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote.