Rational Holes and Asymptotes

• vertical

• 4

• horizontal

• 0

• (-5, -1)

• hole

• (5, 1)

• -4

• (-5,45)

• (5, 25)

What is the vertical asymptote?

• x=-4

• x=1

• x=4

• x=3/2

Match the following for the rational function:

• Vertical Asymptote

• x=2

• y-value of hole

• x=-2

• x-value of hole

• x=3

• Not an asymptote or hole

• y=-4

• Horizontal Asymptote

• y=1

• vertical

• 4

• horizontal

• 0

• (-5, -1)

• hole

• (5, 1)

• -4

• (-5,45)

• (5, 25)

• y = 0

• y = 2

• y = 4

• y = 1/2

• Does Not Exist

• y = 2

• y = 1

• y = -1

• y = 0

• Does Not Exist

• y = 4

• y = 3

• y = -3

• y = 0

• Does Not Exist

• Holes: x = -3
  Vertical: x = 1/2
  Horizontal: y = 0

• Holes: x = 1/2
  Vertical: x = -3
  Horizontal: y = 0

• Holes: Do Not Exist
  Vertical: x = 1/2 and x = -4
  Horizontal: y = 1

• Holes: x = 1/2
  Vertical: x = -3
  Horizontal: y = 1

• Holes: x = -3
  Vertical: x = 1/2
  Horizontal: Does Not Exist

• Only x = 1

• Only x = -1

• Only x = 3

• x = -1 and x = 1

• x = 1 and x = 3

The graph of a rational function will never cross an asymptote.

• True

• False, a graph can cross a vertical asymptote.

• False, a graph can cross a horizontal asymptote because it really dictates the end behavior.