Find all horizontal and vertical asymptotes of the rational function r(x)=(2x−1)(x+3)(3x−1)(x−4).
Since the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote = leading coefficient of the numeratorleading coefficient of the denominator=23. Thus, the horizontal asymptote is y=23.
To determine the vertical asymptotes, we set the denominator equal to .
(3x−1)(x−4)=03x−1=0 and x−4=0Zero Product Property
Thus, the vertical asymptotes are x=13 and x=4.
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