Graphing Rational Functions

• Vertical Asymptote at x = 1

• No Holes

• Horizontal Asymptote at y = 0

• y-intercept at (0, 1/2)

• Vertical Asymptote at x = -3 and x = 1

• Hole at (1, 0)

• Horizontal Asymptote at y = 2

• x-intercepts at (3,0) and (1, 0)

• Vertical Asymptote at x = -1

• No Holes

• Horizontal Asymptote at y = -1/4

• x-intercepts at (0,0) and (-1,0)

• Vertical Asymptote at x = 2

• No Holes

• Horizontal Asymptote at y = -1/3

• y-intercept at (0, 1/2)

• No Vertical Asymptote

• No Holes

• No x-intercept

• Vertical Asymptote at x = 3 and x = -1

• No Holes

• Slant (Oblique) Asymptote at y = x + 5

• y-intercept at (0,0)

Determine the equation of the slant asymptote:  
f(x)= (x²-5x-5)/(x+1)

• y = x - 2

• y = x - 4

• y = x - 6

• y = x + 4

Find the oblique asymptote.
(x² - 2x - 8) / (x - 2)

• y = x

• y = x - 8

• y = x - 4

• y = x + 4

Find the oblique asymptote.
(3x³ - 2x + 1) / (x² + 4x + 2)

• y = 3x

• y = 40x + 25
• y = 3x - 10
• y = 3x - 14

Match the following equations with their x-intercepts.

• x^2 - 2x - 8 = 0

• x= -4, x = 2

• x^2 + 2x - 8 = 0

• x= 2/3

• 3x - 2 = 0

• x= 4, x = -2

• x^2 + 7x - 8 = 0

• x= -8, x = 1