Rational Functions Vertical Asymptotes Holes and Graphs

What creates a hole in the graph of a rational function?

• Crossing the x-axis

• An absence of dirt.

• Crossing a vertical asymptote.

• A factor that cancels out.

What is the horizontal asymptote? 

Mathematical Equivalence

ON

What is the domain?

• All real numbers except 1/2

• All real numbers

• All real numbers except -4

• All real numbers except 4

What is the equation of the rational function graphed?

What are the domain and range?

• D: (−∞, 0) ᴜ (0, ∞)

  R: (−∞, 5) ᴜ (5, ∞)

• D: (−∞, 5) ᴜ (5, ∞)

  R: (−∞, 0) ᴜ (0, ∞)

• D: (−∞, 0) ᴜ (0, ∞)

  R: (−∞, −5) ᴜ (−5, ∞)

• D: (−∞, −5) ᴜ (−5, ∞)

  R: (−∞, 0) ᴜ (0, ∞)

Describe the transformations of the function.

• Shift up by 2 units

  Reflected over the x-axis

• Shift down by 2 units

  Reflected over the y-axis

• Shift up by 2 units

  Reflected over the y-axis

• Shift left by 2 units

  Reflected over the x-axis

Identify Vertical and Horizontal Asymptotes based on the graph

• V.A. --> x = 0

  H.A. --> y = 1

• V.A. --> x = 1

  H.A. --> y = 0

• V.A. --> y = 1

  H.A. --> x = 0

• V.A. --> x = 0

  H.A. --> none

Identify Vertical and Horizontal Asymptotes based on the graph

• V.A. --> x = -1

  H.A. --> y = -1

• V.A. --> x = -1

  H.A. --> y = -2

• V.A. --> y = -1

  H.A. --> x = 2

• V.A. --> x = -1

  H.A. --> y = 2

Identify Vertical and Horizontal Asymptotes based on Graph...

• V.A. --> x = 1/2

  H.A. --> y = -1

• V.A. --> x = -1/2

  H.A. --> y = 1

• V.A. --> y = -1

  H.A. --> x = 1/2

• V.A. --> x = 1

  H.A. --> y = -1