Rationals Discontinuity and Asymptotes

• x = -3

• x = 5

• x = -3 and x = 5

• x = 0

• Does Not Exist

• x = 0

• x = 2

• x = 7

• x = -7

• Does Not Exist

• y = 0

• y = 2

• y = 4

• y = 1/2

• Does Not Exist

• y = 2

• y = 1

• y = -1

• y = 0

• Does Not Exist

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

Label the key features of this rational function:

d

e

removable discontinuity at x=4

removable discontinuity at x=2

vertical asymptote at x=4

horizontal asymptote at x=0

vertical asymptote at x=2

x-intercept at x=4

x intercept at x=2

Where are the discontinuities?

• holes: x=5

  asymptotes: x=3

• holes: x=3

  asymptotes: x=5

• holes: x=-5

  asymptotes: x=-3

• holes: x=-3

  asymptotes: x=-5

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

This equation has 2 discontinuities. Are they . . . . . .?

• Both removable.

  Holes.

• Both non-removable.

  Asymptotes.

• One is removable. One is non-removable.

  An asymptote and a hole.

• There is only one discontinuity.