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

Masaken

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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

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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

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