Monday, April 18, 2016

College Algebra, Chapter 4, 4.6, Section 4.6, Problem 28

Find all horizontal and vertical asymptotes of the rational function r(x)=(2x1)(x+3)(3x1)(x4).

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 .


(3x1)(x4)=03x1=0 and x4=0Zero Product Property


Thus, the vertical asymptotes are x=13 and x=4.

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