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
has a y-intercept of 5 and a slope of 2/3. solve for the standard equation


Whereas we are on the subject of function evaluation we have to now talk about piecewise functions. Actually we've already seen an instance of a piecewise function even if we didn'

how do you round

How do I work this algebra problem step by step (- 1/5) 3 power?

Let's begin with the graph of couple of polynomials. Do not worry regarding the equations for these polynomials.  We are giving these just so we can utilize them to show so

How do you do uniform motion? i am stuck on some problems

1% of what number is 11

a rectangular table is five times as long as it is wide. if the area is 45ft2, find the length and width of the table..

If a jet can travel 600 mph, how long in second will it take the jet to travel 5 miles?