Horizontal asymptote, Algebra

Also, as x obtain very large, both positive & negative, the graph approaches the line specified by y = 0 .   This line is called a horizontal asymptote.

Following are the general definitions of the two asymptotes.

1.   The line x = a is vertical asymptote if the graph rise or fall without bound on one or both sides of the line as x moves in closer & closer to x = a .

2.   The line y = b is horizontal asymptote if the graph approaches y = b as x increases or decreases without bound.  Note that it doesn't have to approach y = b as x BOTH increases and decreases.  Only it needs to approach it on one side in order for it to be a horizontal asymptote.

Determining asymptotes is in fact a fairly simple procedure. First, let's begin with the rational function,

872_Horizontal asymptote.png

where n refer to the largest exponent in the numerator and m refer to the largest exponent in the denominator.

Then we have the given facts regarding asymptotes.

1.   The graph will have vertical asymptote at x = a if the value of denominator is zero at x = a and the numerator isn't zero at x = a .

2.   If n < m then the x-axis is the horizontal asymptote.

3.   If n = m then the line y = a/ b is the horizontal asymptote.

4.   If n > m there will be no horizontal asymptotes.

The procedure for graphing a rational function is somewhat simple. Following it is.

Posted Date: 4/8/2013 2:09:01 AM | Location : United States

Related Discussions:- Horizontal asymptote, Assignment Help, Ask Question on Horizontal asymptote, Get Answer, Expert's Help, Horizontal asymptote Discussions

Write discussion on Horizontal asymptote
Your posts are moderated
Related Questions
find the range of f(x)=2x+4 for the domain {-4,-1,3,4].


what is the greastest common factor of 16x^y^3and 12x

9x^4-x^2=0 step by step

si el log de 28 en base 14 es a cuanto es el log de 16 en base 49

30. 5x-1 greater than 29