Vertical and Horizontal Asymptotes

Find the vertical and horizontal asymptotes for y = (2x-1)/(3x+2)

Vertical:

y = (2x-1)/(3x+2)

3x+2 = 0

3x = -2

x = -2/3

Horizontal:

y = (2x-1)/(3x+2)

y = 2/3

(x^3)/(x^2) = no horizontal

(x^2)/(x^3) = y=0

If f(x) = a(x)/b(x), a(x) and b(x) are functions with no common factors other than 1, and b(x) does NOT equal 0 then:

• f(x) has a vertical asymptote whenever b(x) = 0
• f(x) has at most one horizontal asymptote