Q:

What Is a Horizontal Asympote?

A:

A horizontal asymptote is a line that limits a curve in a particular region of the coordinate plane. In contrast to its vertical counterpart, a horizontal asymptote may be intersected by a curve in a specific set of points but becomes a limiting line everywhere else.

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In algebra, a horizontal asymptote may be defined as a line defined by the formula y = L, where L is the limit of a curve's algebraic equation as its variable approaches infinity. Horizontal asymptotes are best understood in the topic on analytic geometry, where the figure can be viewed as a horizontal line where the algebraic curve does not touch, save for a particular set of points.

To better understand the concept of a horizontal asymptote, the curve must be allowed to approach infinity on both negative and positive ends of the coordinate plane. To calculate the value of L and therefore determine the equation of the horizontal asymptote, the algebraic equation must be presented in the format y, a function of x, or y = f(x). Each term on the x-function must be divided by x raised to the highest exponent and then simplified. Using the mathematical theorem that any non-zero number divided by infinity is equal to zero, the value of x should be substituted by the value of infinity. The results should produce an answer in the form of y = L.

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