Asymptotes

How do you find holes in a rational function?

• Factors that cancel

• Set denominator = 0

• Set numerator = 0

• Substitute 0 for x

What would the horizontal asymptote be for the following rational function:

 $f\left(x\right)=\frac{x^2-4x+3}{x^2-2x+1}$  

•  $y=0$  

•  $y=1$  

•  $y=2$  

• none

How many vertical asymptotes does the function have?

• None

• 1

• 2

• 3

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

• x = 2

• x = -2

• There are no holes.

• x = 5

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

State the vertical asymptote.

• x = -2/5

• x = -5/2

• x = -5

• x = 2

Which asymptote(s) are determined by looking at the denominator?

• vertical
• horizontal
• slant
• none