why can you cross + intersect horizontal asymptotes (1 Viewer)

[Masaken]

but never go near a vertical asymptote? i know it as a 'rule' of sorts when sketching (especially for graphing relations) but i want to know why it's like that, i've never really understood why this is the case

 

[jks22]

I'm not completely sure but here's my thoughts: Vertical asymptotes generally arise because the function doesn't allow particular x-values, but in the case of horizontal asymptotes its generally what the function tends to as it approaches infinity. It doesn't necessarily mean that the horizontal asymptote is not a permissible value, and thus it can intersect

 

[Average Boreduser]

How come a line can cross a horizontal asymptote?

Answer (1 of 2): Firstly, a line is a straight line with an equation like y = 2x + 1 We don’t talk about a curved line we just call it a curve. I think you mean “How come a CURVE can cross a horizontal asymptote?” Secondly, people misunderstand the definition of an asymptote… “A horizontal as...

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