Rational Functions Removable Discontinuities

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

Select all of the true statements.

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

• y = 0
• y = 1/2
• y = 2
• None

Is there a hole on the graph of the function?

• Yes when x = 2

• Yes when x = -2

• No there are no holes.

• Yes when x = 5

• 2

• 3

• -2

• -3

Find the horizontal asymptote.

• None

• y = 0

• y = -1/3

• y = -3

• (-∞,-2) u (-2,6) u (6, ∞)

• (-2,6)

• (-∞,2) u (2,6) u (6, ∞)

• (-∞,2) u (6 ,∞)

The graph of f is shown. Which of the following statements is false?

• 0 removable discontinuities, 1 non-removable discontinuity.

• 1 removable discontinuity, 1 non-removable discontinuity.

• 2 removable discontinuities, 1 non-removable discontinuity.

• 1 removable discontinuity, 2 non-removable discontinuities.