so these things are slightly messing with me, they are the leading coefficents divided provided there both to the nth degree but then how would one get a y=0 ??? i might just be having a massive brainfart but better to ask then to make that mistake on the test👍

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A horizontal asymptote of y=0 occurs when the degree of the numerator is lower than the degree of the denominator, since the denominator will grow much faster than the numerator as x approaches positive or negative infinity. This causes the fraction to approach a value of 0.