Holes of Rational Functions

What is the definition of an ASYMPTOTE?

• A curved line. 
• A line that only touches the origin. 
• A line that only lives on the first quadrant. 
• A line that a curve approaches, as it heads towards infinity. 

The equation of a vertical asymptote is written in the form:

• x=

• y=

• none of the above

Which of the following is determined by just looking at the denominator?

• vertical asymptote
• horizontal asymptote
• holes
• slant asymptote

• x=-5

• x=1/2

• x=-1/2

• x=-3

• x=2

• 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

• x=2

• x=-2

• x=0

• x=-3

• x=6

• x=-7

• x=3