Horizontal+Asymptotes

Kevin: In this page, please explain how to find horizontal asymptotes:

Meredith G-M: To find a horizontal asymptote of a function, find the limit of the function as x approaches infinity and negative infinity. For example, f(x) = 4x/x-3 To find the horizontal asymptotes, find the limit of f(x) as x approaches infinity/negative infinity. limf(x) x-->∞ = 4 and limf(x) x-->-∞ = 4, so there is a horizontal asymptote at y=4

Graph of function:

Paul: Horizontal asymptotes are found by finding the limit as x approaches infinity or negative infinity. When a function approaches infinity or negative infinity, we are examining what is known as the function's end behavior. To learn more about end behavior, click on the following link. http://abcalculus.wikispaces.com/End+behavior

Ari: This is an example of a horizontal asymptote. Its the inverse of tangent: Julie Waters The answer is (C) b= -4. Both graphs hit (5,5)

Sabrina:
 * Unlike a vertical asymptote, a function may cross a horizontal asymptote!

Kevin Wu: example to what sabrina said (aint that a cool looking function) horizontal asymptote x=0, and function crosses the asymptote at... (you do the counting)

horizontal asymptote x=0 crosses at (0,0)

Zach Fusfeld: In addition to what sabrina said, a horizontal asymptote does not occur in the same way that a vertical asymptote occurs. Because it is an endbehavior, both sides of the graph do not need to show a horizontal asymptote. one side of the graph could be approaching infinity whereas the other side has a horizontal asymptote at 1, or anyother point on the graph. one example where this might happen could be in a piecewise function, in fact this is where this would most likely occur

Ben Zielonka: In addition functions(often piecewise) can have one horizontal asymptote as x approaches positive infinity and a different one as x approaches negative infinity. This can be seen in Ari's graph of arctan.