Question

Find the vertical, horizontal, and slant asymptotes, if any, for f(x)= (5x^3 + 49x^2 + 127x + 75)/(x^2 + 9x + 18)

Answer 1

For vertical asymptote set denominator equal to zero and solve for x. And that is here you have vertical asymptotes

Answer 2

vertical --> set denominator to 0
horizontal --> highest exponent on top...thus no horizontal asymptote exists
slant --> use long division, asymptote is quotient ignoring the remainder

Answer 3

For the vertical asymptotes I got -3 and -6, but this isn't an answer choice.

Answer 4

And for slant I got y=5x+4

Answer 5

slant is correct
the vertical is correct too, however -3 doesnt work because it is also a zero for top as well
this gives a 0/0 situation so x=-3 is undefined

Answer 6

ohhhh okay. thank you!

Answer 7

yw, actually i should be more specific, it makes a hole at x=-3