Question

r(x)= x(x-3)^2/(x+3)^3
How do I find domain
vertical Asyptotes
Hort/Obliq

Answer 1

in this rational expression, vertical asymptotes occur at the values of x where the denominator is zero...., ie, \(\large (x+3)^3=0 \).... solve for x here for your vertical asymptotes...

Answer 2

domain are those values of x for which y is defined and unique

Answer 3

once you find your vertical asymptotes, they give you a clue as to what your domain is... it is the x values that give back a numeric value for y.....

Answer 4

horizontal/oblique asymptotes cannot occur at the same time, so you either have 1 or the other, or none at all...

Answer 5

oblique asymptotes occur only when the degree of the numerator is exactly 1 more than the degree of the denominator.

Answer 6

horizontal asymptotes occur when the degree of the numerator is equal to or less than the degree of the denominator...

that being said, can you tell me if you have horizontal or oblique asymptotes?

Answer 7

degree of num. is 3 & deg. of den is also 3
thus deg. of num - deg of den =0

Answer 8

therefore it will have horizontal asymptote