Explain why the graph of a non-piecewise function with avertical asymptote canno

Question

Explain why the graph of a non-piecewise function with avertical asymptote cannot intersect that asymptote, but if it has ahorizontal/polynomial asymptote, it acn intersect that asymptote.Use at least two examples of functions that don't cross verticalasymptotes but do cross a horizontal/polynomial asymptote. thanks for the help Explain why the graph of a non-piecewise function with avertical asymptote cannot intersect that asymptote, but if it has ahorizontal/polynomial asymptote, it acn intersect that asymptote.Use at least two examples of functions that don't cross verticalasymptotes but do cross a horizontal/polynomial asymptote. thanks for the help

Explanation / Answer

I'm sorry that I can't think of examples off the top of my head butI'll provide the best explanation I can. A vertical asymptote is avalue of x in which a function is undefined, meaning a division byzero. This is not possible in mathematics and thus we cannot have afunction intersecting its own vertical asymptote. For a horizontalasymptote, the function tends to go to that value as x approachesinfinity, or in some cases negative infinity, or both (Note: afunction can have more than one h. asymptote; Ex: y=arctan(x), forall real x). Thus, x can intersect that asymptote anywhere withinits domain. Hope this helps!

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