Question

Under what conditions does a rational function have vertical, horizontal and oblique asymptotes?

use limits..

Answer 1

it says on my book:
f(x)=g(x)/h(x)
Conditions for vertical asymptote:
h(x)=0 must have at least one solution s, and lim(x-> infinity) f(x)=inifinity

conditions for horizontal asymptote:
lim(x-> infinity) f(x)= k, where k is all real numbers

--> can you just explain it further?

Answer 2

@agent0smith

Answer 3

Vertical asymptotes are when the denominator is zero - since you can't divide by zero

Horizontal asymptotes are a bit more complex since they involve end behaviour... look at the highest powers of x on the numerator and denominator to find the horiz. asymptotes.

If the numerators highest power is smaller than the denominators, eg 3x^3 and 4x^5, the asymptote is y=0.
If the numerator and denominator have the same highest power, the asymptote is the the ratio of the coefficients... eg 3x^2 and 5x^2... y=3/5



Oblique or slant asymptotes come from the numerator having a greater highest power than the denominator... you have to use long division to find the slant asymptote.

Answer 4

I'd explain using limits but i don't have time...

Answer 5

ok thanks!, i will just read what you wrote..

Answer 6

i already know that from grade 11, i just don't know how to explain it using limits..

Answer 7

Horizontal asymptotes

lim x => inf, y => (the value of the horiz. asymptote)

verticals:

lim x => (a value that gives a denominator of zero), y => + or - infinity

etc, but i gotta go.

Answer 8

ok, thanks for ur time(^_^)