How do you find the slant asymptote of #f (x ) = (3x^2 - 2x - 1) / (x + 4 )#?

Answer 1

Slant asymptote is given by #y=3x#

The vertical asymptotes of #(3x^2-2x-1)/(x+4)# are given by zeros of denominator i.e. #x+4=0#.

As the degree of numerator is just one higher than that of denominator, there is no horizontal asymptote, but we do have a slant asymptote given by #y=(3x^2)/x=3x#.

The slant asymptote is given by #y=3x#

graph{(3x^2-2x-1)/(x+4) [-30, 40, -100, 100]}

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Answer 2

Elias Ackerman

To find the slant asymptote of the function (f(x) = \frac{3x^2 - 2x - 1}{x + 4}), divide the numerator by the denominator using polynomial long division or synthetic division. The quotient obtained represents the equation of the slant asymptote.

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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.