Rational Functions

Which is the function of the graph?

Answer explanation

What is the domain of the function?

Find the excluded value(s) in the domain.

• 3

• -3

• 0

• -1

Find the vertical asymptote(s).

• None

• x = 0

• x= 4

• x = -4, 4

Find the horizontal asymptote.

• None

• y = 0

• y = -1/3

• y = -3

Find the hole(s).

• None

• x = -4

• x = 4

• x = 1/2

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

State the vertical asymptote:  f(x)=(x-2)/(x+5).

• x = -2/5

• x = -5/2

• x = -5

• x = 2

State the horizontal asymptote:  (2x²-5x +1)/(x²-x)

• y = 2

• y = 1

• y = 0

• There is no HA

Determine the coordinates of the hole on the graph of 
f(x)= (x²-2x + 1)/(x²+2x - 3)

• (1, 1/3)

• (-1, -1/3)

• (1, 0)

• (1, -3)