fx x2x12x5 a state the Domain b Vertical Asymptetos c Horiz

f(x) = (x^2-x-12)/(x-5)

(a) state the Domain

(b) Vertical Asymptetos

(c) Horizontal or slant Asymptotes.

Solution

given

f(x) = (x^2 -x -12) /(x-5)

domain is what values of \'x\' that f(x) can have

in this here at x=5 , f(x) = (25 -5-12) /5-5 = 8/0 = infinite

so we have to exclude \'5\' from domain

domain = R - {5} = { all numbers } - 5

domain x is not equal to \'5\'

x != 5 (domain)

b). vertical Asymptetos

x=5

c).

First we must compare the degrees of the polynomials. The numerator contains a 2nd degree polynomial while the denominator contains a 1st degree polynomial.

Since the polynomial in the numerator is a higher degree than the denominator, there is no horizontal asymptote. There is a slant asymptote instead.