Question

What do you do to solve for the point in which a graph crosses a horizontal asymptote? I'm very confused please help

Answer 1

A horizontal asymptote happens in a function f(x) when NO x value can make the function equal to that value.

For example the function f(x) = 1/x has an asymptote at y = 0 because the function can never = 0 no matter what x is.

To find it, one would take the limit of f(x) as x approaches infinity and negative infinity to find these values

Answer 2

I know how to find the horizontal asymptote, of course it depends on the degrees of both the numerator and denominator. I'm confused on how to find the point of where a line might cross a horizontal asymptote in a situation where it did. Is it true that you have to set the whole euqation equal to the horizontal asymptote and solve for x and then the point that you solved for and the HA would be where you cross the horizontal asymptote? I'm so confused I'm not sure if this is right or not and I have a quiz on it tomorrow ;/

Answer 3

the line (or function) can never cross horizontal asymptotes

Answer 4

Umm I know it can...the line/function can never cross a vertical asymptote however it is true that a line/function can cross a horizontal asymptote ONCE

Answer 5

We just learned that in math. A line/function can cross a horizontal asymptote once and only once in a function at the most. It doesn't have to but it is most definitely possible.

Answer 6

I just need to know how to find the point where it does cross the horizontal asymptote

Answer 7

Whereas vertical asymptotes are sacred ground, horizontal asymptotes are just useful suggestions. Whereas you can never touch a vertical asymptote, you can (and often do) touch and even cross horizontal asymptotes. Whereas vertical asymptotes indicate very specific behavior (on the graph), usually close to the origin, horizontal asymptotes indicate general behavior far off to the sides of the graph. To get the idea of horizontal asymptotes, let's looks at some simple examples ~ via Purple Math

Answer 8

ok, i see

Answer 9

sorry for misleading you. I didn't consider a whole family of functions.

you would set the equation to the HA like you said and solve for x. if x exists (isnt only for infinty like the limit said) it crosses

Answer 10

Yeah:/ i wish they couldn't! I just don't know how to find that point of intersection between the actual function and the asymptote. I have been told that you set the equation equal to the horizontal asymptote and then you solve for x and so your point would be x,HA but idkkkkk

Answer 11

yes. that is correct. if x exists (from solving), the function crosses the asymptote (which isn't in effect yet). if x doesn't exist (gives you infinity or something divided by zero), it doesn't cross

Answer 12

Ok thanks for clearing that up:) Helps a lot!!!

Answer 13

thanks for reminding me the case existed :)
glad i could help

Answer 14

basically, (usually for rational functions with powers), if you get multiple possible solutions for x, all you have to do is plug it back in the original equation and exclude the extraneous solutions.