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
graph the following and find the point of intersection 2x+y=-4 y+2x=3

We've been talking regarding zeroes of polynomial and why we require them for a couple of sections now. However, we haven't really talked regarding how to actually determine them f

Multiply 2(b + 5) Thanks


The reduced row echelon form of  is equal to R =   (a)  What can you say about row 3 of A? Give an example of a possible third row for A. (b)  Determine the values of


The "humps" where the graph varies direction from increasing to decreasing or decreasing to increasing is frequently called turning points .  If we know that the polynomial con

Gauss-Jordan Elimination Next we have to discuss elementary row operations. There are three of them & we will give both the notation utilized for each one as well as an instanc

how would i solve one of these functions. like how would i find the domain and range? and may i get an example.

2x+y/x+3y=-1/7and 7x+36y=47/3 hence find p if xy=p=x/y