Determine the asymptotes of x^2 + 2x - 3 / (x + 4)

[pencile]

Determine the asymptotes of x^2 + 2x - 3 / (x + 4)

I'm struggling to work out the horizontal asymptote for this question.

For the vertical asymptote, I get that
x -> -4, y -> infinity
x = -4.

The other answer is y = x - 2. From doing long division I get
x - 2 + (5 / (x + 4)).

I'm not sure how this leads to x - 2 being the horizontal asymptote. Thanks for helping.

 

[stapel]

Determine the asymptotes of x^2 + 2x - 3 / (x + 4)

I'm struggling to work out the horizontal asymptote for this question.

For the vertical asymptote, I get that
x -> -4, y -> infinity
x = -4.

The other answer is y = x - 2. From doing long division I get
x - 2 + (5 / (x + 4)).

I'm not sure how this leads to x - 2 being the horizontal asymptote. Thanks for helping.

Since "y = x - 2" is not a horizontal line then, no, this cannot be a horizontal asymptote. It is, however, a slant asymptote.

To learn what these are and how to compute them, try here.

 

[pencile]

Since "y = x - 2" is not a horizontal line then, no, this cannot be a horizontal asymptote. It is, however, a slant asymptote.

To learn what these are and how to compute them, try here.

That was helpful. Thanks.

 

[pencile]

Found this:

y = p(x)/q(x)
if degree of p(x) < degree q(x), y = 0 is an asymptote
if degree of p(x) = degree q(x), y = a/c is an asymptote
if degree of p(x) = degree q(x) + 1, y = mx + c (non-remainder part of long division) is an asymptote

For the benefit of others who are confused as well.