Applying and analysing functions

This rational function has a vertical asymptote at...

• x = 2

• x = 0

• y = 0

• x = -2

Identify the horizontal and the vertical asymptotes of the function shown in the graph.

• horizontal asymptote: y = -3; vertical asymptote: x = -4
• horizontal asymptote: x = 3; vertical asymptote: y = -4
• horizontal asymptote: y = -3; vertical asymptote: x = 4
• horizontal asymptote: x = -3; vertical asymptote: y = 4

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

• vertical
• horizontal
• end behavior
• none

What is the Vertical Asymptote? 

• x= -5
• x= 5
• x= 6
• x= -6

what are the asymptotes for this graph?

•  $y=3,\ \ no\ vertical\ asymptote$ 

•  $x=0,\ no\ horizontal\ asymptote$ 

•  $y=3,\ x=0$ 

•  $y=0,\ x=3$ 

What is the horizontal asymptote in the function  $f\left(x\right)=\frac{3x-2}{2x^2-8x+1}$  
Think: Which case is this?

• y = 0

• y = -2

• y = 1

Fill in the blanks: The line x = 0 is the  _________   _________ of the graph of $f\left(x\right)=\ \frac{1}{x}$ .

• horizontal asymptote

• vertical asymptote

• y-intercept

• x-intercept

What is the asymptote of the following graph?

• y = 0

• x = 0

• y = -4

• x = -4

 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.  

What is the asymptote?

• y = 2

• y = 3