asymptotes?

Question

1. Explain what a horizontal asymptote is and how to find one for a given function.

Answer 1

x^-1 ....
or 1 over x.
as long as x is not equal to zero (undefined) the solution is never equal to zero (a fraction)
a horizontal asymtope exist at y = 0

e^-x same thing

Answer 2

If a function approaches a particular value but never really gets there for any apparent value of the independant variable, the line marking that particular value is the horizontal asymptote of the function.
Let me illustrate this, consider a graph y=f(x)
y does not equal a certain value k for any value of x, though it seems to be getting close to it. Then it is said that y=k is a horizontal asymptote of y=f(x)

Basically if you can show that either f(x) > k OR f(x) < k and k is the closest value to the actual values of the function that such an inequality will hold then k is the horizontal asymptote required.

How you show this will depend on the composition of the functions appearing in the function f(x) that you may consider.

Hope this helps!!

Answer 3

An asymptote is a graphic for a given function or a certain part of a graphic of a function.

An example of an asymptote is for the function f(x)=1/x.
for x=1, f(x)=1;
for x=2, f(x)=1/2=0,5;
for x=3, f(x)=1/3=0,33;
for x=4, f(x)=1/4=0,25;
etc
meaning that you get closer and closer to a certain value (in this case it's 0), but you never reach it. The function's graphic will be a curve line heading towards Ox (your graphic is in the xOy coordinates, Ox is horzintal, Oy is vertical) but only "touching" it at infinite.

Hope it helps! :) Good luck with your math! I also had problems with asymptotes, but believe me, it gets worse!

Answer 4

An asymptote is a line which a curve approaches, but never touches. For example, y = 2^x goes closer and closer to the x axis, but never touches it. And the person above me explained how to find it, so there isnt much point in me explaining it too.