Asymptote and Holes Practice

• No vertical asymptotes.

• One vertical asymptote: x = 4

• Two vertical asymptotes: x = -3 and x = -7

• Three vertical asymptotes:  x = -3, x = 4, and x = -7

The holes of a rational function occur when :

• my pencil pokes a hole in the paper I'm working on

• there is something left in the denominator

• the value of f(0)

• a factor in the denominator cancels with a factor in the numerator

• 2

• -2

• -6

• 6

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

Find the vertical asymptote.

• y=2/3

• x=3/2

• x= 2/3

• x=1/3

Find the coordinates of the hole.

• (-3, -3)

• (-3, 3)

• (3, -3)

• (3, 3)

Find the horizontal or slant asymptote.

• y = x

• y = x - 8

• y = x - 4

• y = x + 4

Where is the horizontal asymptote?

• y= 5

• y= 0

• y= 1

• y= 6

Find the slant asymptote.

• y = 3x - 12

• y = x + 5

• y = 3x - 5

• y = 3x - 7

Find the slant asymptote. (x² - 2x - 8) / (x - 2)

• y = x

• y = x - 8

• y = x - 4

• y = x + 4