Rational Functions and Asymptotes

Find the vertical asymptotes and holes of the function.

• Holes: None;

  VA: x = 1, -3

• Holes: x = -3;

  VA: x = 1

• Holes: x = -3, 1

  VA: None

• Holes: x = 1

  VA: x = -3

Where is there a hole on the graph of the function?

• x = 2

• x = -2

• There are no holes.

• x = 5

State the vertical asymptote.

• x = -2/5

• x = -5/2

• x = -5

• x = 2

What are the Vertical Asymptotes of...

• x = 0, -5

• x=0, 5

• x = 2, -7

• x = -2, 7

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

• vertical asymptote

• horizontal asymptote

• holes

• slant asymptote

• 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

Find the vertical asymptote.
g\left(x\right)=\frac{\left(x+3\right)\left(x-2\right)}{\left(x+5\right)\left(2x-1\right)}

• x=-5

• x=1/2

• x=-1/2

• x=-3

• x=2

Find the vertical asymptote(s).

• None

• x = 0

• x= 4

• x = -4, 4

Identify the vertical asymptote(s).

• x=0

• x=-3

• x=6

• x=-7

• x=3

Find the vertical asymptote.

• y=2/3

• x=3/2

• x= 2/3

• x=1/3