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How do you find the asymptotes for #f(x) = (x+6)/(2x+1)#?

Answer 1

Lincoln Anderson

vertical asymptote at # x = -1/2#
horizontal asymptote at # y = 1/2 #

Vertical asymptotes are found when the denominator of

the rational function is zero.

This will occur when 2x + 1 = 0 , hence 2x = - 1

vertical asymptote is : # x = -1/2 #

[ Horizontal asymptotes can be found when the degree of

the numerator and the degree of the denominator are equal.]

In this question they are both of degree 1 and so a

horizontal asymptote exists.

The asymptote is found by taking the ratio of leading coefficients.

horizontal asymptote is ; # y = 1/2 #

graph{(x+6)/(2x+1) [-20, 20, -10, 10]}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.