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How to find horizontal asymptotes

How to Find Horizontal Asymptotes|Before we get into the details of How to find horizontal asymptotes, let’s Figure out what Horizontal Asymptotes is? On a graph, a horizontal asymptote is a y-value that a function approaches but never reaches. Here’s a simple graphical representation of How To Find Horizontal Asymptotes Using a graphed function that approaches, but never quite achieves, y=0.


How to Find Horizontal Asymptotes: Basic Rules

These two rules should be memorized before learning “How to Find Horizontal Asymptotes.”

  • If the denominator’s degree (the biggest exponent) is greater than the numerator’s degree, the horizontal asymptote is the x-axis (y = 0).
  • If the numerator’s degree is greater than the denominator’s degree, there is no horizontal asymptote.

The following mnemonic device can help you recall the rules of “How to Find Horizontal Asymptotes”:  BOBO BOTN EATS DC

  • BOBO – Bigger on the bottom & y=0
  • BOTN – Bigger on the top, none
  • EATS DC – Exponents Are The Same—Divide Coefficients

How to Find Horizontal Asymptotes: Examples 

Let’s look at a few examples to better understand how to find horizontal asymptotes.

Example 1: How to Find Horizontal Asymptotes of 

fx=4xx-3

Solution: y=4

 Because the degrees are the same, divide the numerator and denominator leading coefficients        41  = 4

Example 2: How to Find Horizontal Asymptotes of 

gx=5x2x+3

Solution: None, because the numerator’s degree is greater than the denominator’s degree.


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Frequently Asked Questions (FAQs)

How many horizontal asymptotes are there in a rational function?

Only one horizontal
A rational function can have one oblique or horizontal asymptote and numerous alternative vertical asymptotes, all of which can be determined.

How many horizontal asymptotes does an Arctan have?

Two asymptotes on the horizontal
There are two horizontal asymptotes on the graph of y=arctan x.

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