Determine the horizontal asymptote for r(x) = x^3-2x^2+3 / x-2, if one exists.
a) there is no horizontal asymptote.
b) the horizontal asymptote is y = 0.
c) the horizontal asymptote is x = 2.
d) the horizontal asymptote is y = x - 1.

Step-by-step explanation:

A horizontal asymptote exists for this function at y = 0.

Compare the degrees of the numerator and denominator

If N < D, then y = 0 is the horizontal asymptote.

If N = D, then y =  

a

b

(a = leading coefficient numerator and b = leading coefficient denominator).

If N > D, then there is no horizontal asymptote.

If N > D by only one, then there is a slant asymptote.

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option