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The Question & Answer (Q&A) Knowledge Managenet

The Internet has many places to ask questions about anything imaginable and find past answers on almost everything.

Table of Contents

- Why do polynomials not have Asymptotes?
- Why do slant asymptotes occur?
- What are the three types of Asymptotes?
- What does a slant asymptote look like?
- Can you have a slant and horizontal asymptote?
- What is the rule for horizontal asymptote?
- Can you have two horizontal asymptotes?
- Can there be two vertical asymptotes?
- Can a function have 3 Asymptotes?
- What are the 8 types of functions?

Rational algebraic functions (having numerator a polynomial & denominator another polynomial) can have asymptotes; vertical asymptotes come about from denominator factors that could be zero. It has no asymptotes because it is continuous on its domain, which means there are no holes or jumps.

A slant (oblique) asymptote occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator. To find the slant asymptote you must divide the numerator by the denominator using either long division or synthetic division.

There are three kinds of asymptotes: horizontal, vertical and oblique. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. Vertical asymptotes are vertical lines near which the function grows without bound.

The oblique or slant asymptote is found by dividing the numerator by the denominator. A slant asymptote exists, since the degree of the numerator is 1 greater than the degree of the denominator. The equation = is a slant asymptote.

A graph can have both a vertical and a slant asymptote, but it CANNOT have both a horizontal and slant asymptote. You draw a slant asymptote on the graph by putting a dashed horizontal (left and right) line going through y = mx + b.

The three rules that horizontal asymptotes follow are based on the degree of the numerator, n, and the degree of the denominator, m. If n < m, the horizontal asymptote is y = 0. If n = m, the horizontal asymptote is y = a/b. If n > m, there is no horizontal asymptote.

A horizontal asymptote for a function is a horizontal line that the graph of the function approaches as x approaches ∞ (infinity) or -∞ (minus infinity). There are literally only two limits to look at, so that means there can only be at most two horizontal asymptotes for a given function.

A graph can have an infinite number of vertical asymptotes, but it can only have at most two horizontal asymptotes. The graph of y = f(x) will have vertical asymptotes at those values of x for which the denominator is equal to zero.

There are three kinds of asymptotes: horizontal, vertical and oblique. A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes. Vertical asymptotes occur at singularities of a rational function, or points at which the function is not defined.

The eight types are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal.