Does a horizontal line have horizontal asymptotes?

  • Thread starter Esoremada
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  • #1
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For example, y = 7. Are there an infinite number of asymptotes at any y value that isn't 7? If so, how would I format this statement on my homework?

*edit* oops sorry, I meant to post this in homework help
 

Answers and Replies

  • #2
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I don't think so.

Asymptotes are usually defined as lines that a given function approaches infinitely close, but never reaches. Under this definition, a line has no asymptotes.
 
  • #3
pwsnafu
Science Advisor
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Asymptotes are usually defined as lines that a given function approaches infinitely close, but never reaches.
Except functions like ##\frac{\sin x}{x}## cross their asymptote an infinite number of times.

Formal definition from Wikipedia:
Let ##A:(a,b)\rightarrow\mathbb{R}^2## be a parametric curve, in coordinates ##A(t)=(x(t),y(t))##. Suppose the curve tends to infinity, that is:
##\lim_{t\rightarrow b}(x^2(t)+y^2(t))=\infty##.
A line ##\mathcal{l}## is an asymptote of A if the distance from A(t) to ##\mathcal{l}## tends to zero as ##t\rightarrow b##
This is really iffy. You could argue either way.
 

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