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
ron the realtor is offered a job directly out of real-estate school. he has a choice as to which way he will receive his salary the first year. salary plan 1: he would receive a

A team needs to save up $400 for new uniforms and currently has $190. They decide to hold a fundraiser where they can earn a $7 profit for each item sold. What equation could be s

Solve out the following system of equations by using augmented matrices. 3x - 3 y - 6 z = -3 2x - 2 y - 4 z = 10 -2x + 3 y + z = 7 Solution Following is the au

A student rented a bicycle for a one-time fee of $12.00 and then a charge of $0.85 per day.She paid $28.15 for the use of the bicycle. How many days did she keep it?

Use (fog)(4), (gof)(4), (fog)(x), and (gof)(x) 1.) f(x)=x^2+1 and g(x)=x+5

1. Find out all the zeroes of the polynomial and their multiplicity.  Utilizes the fact above to find out the x-intercept which corresponds to each zero will cross the x-axis or on

find th e parent function g(x) = -(x + 8)2 + 4