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## How do you find a horizontal asymptote?

**To find horizontal asymptotes:**

- If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
- If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

## How do you find the vertical and horizontal asymptotes of a domain?

Find the domain, horizontal asymptotes of a rational function

## How do you find the vertical and horizontal asymptotes of a graph?

The graph will have a vertical asymptote at x=a if the denominator is zero at x=a and the numerator isn’t zero at x=a . If n<m then the x -axis is the horizontal asymptote. Ifn=m then the line y=ab y = a b is the horizontal asymptote. If n>m there will be no horizontal asymptotes.

## What are the rules for horizontal asymptotes?

**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.

## How do you find Asymptotes?

**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 are vertical asymptotes and holes?

We’ll say it again, since it’s important: Vertical asymptotes occur at roots (a.k.a. zeros) of the denominator after the rational function has been simplified; holes occur at roots of the denominator that cancel out entirely during the simplification.

## Is there a vertical asymptote at a hole?

Holes occur when factors from the numerator and the denominator cancel. When a factor in the denominator does not cancel, it produces a vertical asymptote. Both holes and vertical asymptotes restrict the domain of a rational function.

## Are domain and vertical asymptotes the same?

A vertical asymptote represents a value at which a rational function is undefined, so that value is not in the domain of the function. A reciprocal function cannot have values in its domain that cause the denominator to equal zero.

## What is a vertical asymptote?

Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function. (They can also arise in other contexts, such as logarithms, but you’ll almost certainly first encounter asymptotes in the context of rationals.)