Properties of Rational Functions

 Identify any horizontal asymptotes. 
 $f\left(x\right)=\frac{1}{x^2-\ 3x\ }$  

•  $y=0$  
  

•  $y=1$  
  

•  $y=0$  
   $y=3$  
  

• There are no horizontal asymptotes.  

Tags

CCSS.HSF-IF.C.7D

 Identify any vertical asymptotes. 
 $f\left(x\right)=\frac{1}{x\left(x-3\right)\ }$  

•  $x=0$  
   $x=3$  
  

•  $x=0$  
   $x=-3$  
  

•  $y=0$  
   $y=3$  
  

• There are no vertical asymptotes.  

Tags

CCSS.HSF-IF.C.7D

What is the vertical asymptote?

• x= -2

• x= 2

• x= 0

• x= 1

Tags

CCSS.HSF-IF.C.7D

What is the horizontal asymptote of this function?

• y=2
• x=1/2
• y=1
• y=1/2

Tags

CCSS.HSF-IF.C.7D

 $f\left(x\right)=\frac{x-2}{x+5}$  

State the vertical asymptote.

• x = -2/5

• x = -5/2

• x = -5

• x = 2

Tags

CCSS.HSF-IF.C.7D

 Identify any vertical asymptotes. 
 $f\left(x\right)=\frac{1}{x^2-\ 4\ }$  

•  $x=-2$   
  

•  $x=2$  
   $x=-3$  
  

•  $x=2$  
   $x=-2$  
  

• There are no vertical asymptotes.  

Tags

CCSS.HSF-IF.C.7D

 Identify any horizontal asymptotes. 
 $f\left(x\right)=\frac{2x^2+2x-12}{x^2-\ 4\ }$  

•  $x=2$  
   $x=-2$  
  

•  $y=2$  
  

•  $y=0$  
  

• There are no horizontal asymptotes.  

Tags

CCSS.HSF-IF.C.7D

What is the horizontal asymptote to this function?

• y=4
• y=0
• y=-2
• y=1

Tags

CCSS.HSF-IF.C.7D

What is the horizontal asymptote?

• y=3

• y=2

• x=1

• y=1

Tags

CCSS.HSF-IF.C.7D

What is the horizontal asymptote?

• y = -4
• y = 1
• x = 1
• y = -6

Tags

CCSS.HSF-IF.C.7D