Holes of Rational Functions

Find the vertical asymptotes and holes of the function.

• Holes: None;

  VA: x = 1, -3

• Holes: x = -3;

  VA: x = 1

• Holes: x = -3, 1

  VA: None

• Holes: x = 1

  VA: x = -3

Answer explanation

Identify the x-value of the hole(s).

• x=0

• x=-3

• x=6

• x=-7

• x=3

Find the vertical asymptote(s), hole(s) and horizontal asymptote.

• V.A.: x = -1
  Holes: x = 2
  H.A.: None

• V.A.: x = 2
  Holes: x = 1
  H.A.: None

• V.A.: x = -1
  Holes: x = 2
  H.A.: y = 1/4

• V.A.: x = 2, -1
  Holes: x = None
  H.A.: None

• (2, 0)

• (2, 3)

• (-2, -3)

• (-2, -1)

• (3, 2)

• (3, 0)

• (-3, -2)

• (-3, -1)

• (-2, -5)

• (2, 4)

• (-2, 0)

• (2, 5)

Identify the x-value of the hole(s).

• x=0

• x=-3

• x=6

• x=-7

• x=3

• 2

• -2

• -6

• 6

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5