Basic Rational Functions

Basic Rational Functions

Rational Functions

• What is a Rational Function?

• How to determine Zeros

• Finding Vertical and Horizontal Asymptotes

• Locating Holes

A Hole will occur when N(x) and D(x) are both zero for a given value.

Example: $f\left(x\right)=\frac{3\left(x-5\right)\left(x+1\right)}{\left(x-5\right)\left(x+2\right)}$  

Find all Zero's , Vertical and Horizontal Asymptototes, and Holes

Multiple Choice

What is/are the x-intercepts of this graph?

• (-2,0) and (2,0)
• (-2,0)
• (3,0)
• (2,0) and (3,0

Multiple Choice

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

• vertical
• horizontal
• slant
• none

Multiple Choice

What are the asymptotes?

• x = -2 and y = -1

• x = -2 and y = 1

• x = 2 and y = 1

• x = 2 and y = -1

Multiple Choice

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

Multiple Choice

Find the horizontal asymptote.

• None
• y = 0
• y = -1/3
• y = -3

Multiple Choice

What is the Vertical Asymptotes? 

• x= -5
• x= 5
• x= 6
• x= -6

Multiple Choice

What is the hole?

• x= 4
• x= -4
• x= 5
• x= -5

Multiple Choice

What are the Vertical Asymptotes of...

• x = 0, -5
• x=0, 5
• x = 2, -7
• x = -2, 7