Asymptotes and Discontinuities

What is the Vertical Asymptotes? 

• x= -5

• x= 5

• x= 6

• x= -6

Find the horizontal asymptote.

• None

• y = 0

• y = -1/3

• y = -3

Where is the removable discontinuity?

• x=2

• x=2 and x=3

• x=-3

• x=3

Where are the discontinuities?

• holes: x=-3

  asymptotes: x=-1

• holes: none

  asymptotes: x=-1

• holes: x=-1

  asymptotes: x=-3

• holes: x=-1

  asymptotes: none

Label the key features of this rational function:

d

e

horizontal asymptote at x=0

x-intercept at x=4

removable discontinuity at x=4

removable discontinuity at x=2

vertical asymptote at x=2

vertical asymptote at x=4

x intercept at x=2

Determine whether the graph of the function has a vertical asymptote or a removeable discontinuity at x = -1.

• Vertical Asymptote

• Discontinuity

• Bob, bob, bob

• Infinite

• 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

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Determine the type(s) and location(s) of discontinuities

• infinite at x = ∞.

• jump at x = -∞, removable at x = 2.

• the graph is continuous (no discontinuities)

• infinite at x = ∞, removable at x = 0

Determine whether the graph of the function has a vertical asymptote or a removeable discontinuity at x = -1.

• Vertical Asymptote

• Discontinuity

• Hump Day

• Infinite