Doug C. answered • 03/16/19
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Yes. Consider a function like f(x)= (x-3)(x+7)/(x3+1).
The limit as x->+/- inf is 0, i.e. horizontal asymptote y = 0, but the graph crosses its horizontal asymptote at (3,0) and (-7,0).
Doug C.
A rational function can cross its horizontal asymptote. The test is to determine the y value of the horizontal asymptote, then set the function equal to that value and solve for x. If that process results in a real number, then indeed the function crosses its horizontal asymptote at that x-value. As x approaches positive or negative infinity , the y values of the function get closer and closer to the horizontal asymptote. Here is an example of the above: desmos.com/calculator/nav35scxz0
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04/13/23
Lauren S.
I just had a student with the same question.... But mine was (2x+8)/(3x^2+3x-18), y=0 horizontal asymptote but a x=-4 intercept. Isn't the definition of an asymptote mean that the function CANNOT cross that line? Is there some type of exception for horizontal asymptotes? I'm just a physicist, I don't know WHY this would be the case.04/13/23