Question

Find the vertical, horizontal, and oblique asymptotes, if any, for f(x)= 5x^3+41x^2+44x+8/x^2+8x+7

sorry this looks so difficult, if you could help explain how to figure out different asymptotes, that would be great. thanks :)

Answer 1

there is no horizontal asymptote, because the degree of the numerator (3) is larger than the degree of the denominator (2)

Answer 2

vertical asymptote, set
\[x^2+8x+7 =0\] and solve for \(x\)
this one factors, so it is not that hard

Answer 3

oblique asymptote: divide
you will get a quotient and a remainder
forget the remainder, the quotient is a line, it is your oblique asymptote

Answer 4

the vertical asymptote is not zero

Answer 5

Thank you both so so much!! :)

Answer 6

Good Luck!

Answer 7

thanks :)