How do I find the vertical and horizontal asymtope?

Question

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

Answer 1

The rational function

To find vertical asympotote, solve the denominator for 0.

x - 2 = 0

x = 2

Vertical asymptote is  x  = 2 .

To find horizontal/slant asymptote, first find the degree of the numarator and  the degree of denominator.

Degree of the numarator =1 and the degree of denominator = 1.

Since the degree of the numerator is equal to the degree of the denominator, it is horizontal asymptote.

Horizontal asymptote is the ratio of the leading coefficient of numarator and denominator.

Leading coefficient of numarator =   -2, leading coefficient of denominator = 1

y  = -2/1

y  = -2 is the horizontal asymptote.