What are the asymptote of?

Question

f(x)=x^2+12x+4 / 2x+4

like slant and/or vertical

Answer 1

vertical asymptotes occur when your denominator equals zero. In this case when x = -2, you have a vertical asymptote.

this one has a slant as well due to the fact that the degree of the numerator is greater than the denominator

to find the slant you must divide the fraction and whatever you get for your QUOTIENT is the slant asymptote.

(x² + 12x + 4) ÷ (2x + 4) = (1/2)x + 5 - 16/(2x + 4)

I did this by synthetic division, hopefully you can do that. You can also use long division. The quotient is the only thing I care about...

y = (1/2)x + 5 is your slant and x = -2 is your vertical