Rational Functions

• x=5

• x=2

• y=1

• y=0

• x=-5

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$   

• 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

What is the x-value of the hole? $g\left(x\right)=\frac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)\left(x-2\right)}$  

• 2

• -2

• -6

• 6

• A hole occurs where x=-3

• Horizontal asymptote at y=0

• vertical asymptote at x=5

• There is no horizontal asymptote

State the vertical asymptote: 

 $g\left(x\right)=\frac{\left(x+2\right)}{\left(2x+3\right)}$  

• x=2

•  $x=\frac{2}{3}$  
  

•  $x=-\frac{2}{3}$  
  

• x=-2

•  $x=-\frac{3}{2}$  

 $h\left(x\right)=\frac{x\left(x-3\right)\left(x-6\right)\left(x+3\right)}{3x\left(x+3\right)\left(x-6\right)\left(x+7\right)}$  

Identify the x-value of the hole(s).

• x=0

• x=-3

• x=6

• x=-7

• x=3

What is the hole?

• x= 4
• x= -4
• x= 5
• x= -5

What is the Vertical Asymptotes? 

• x= -5
• x= 5
• x= 6
• x= -6

What are the asymptotes?

• x=-3, y=1
• x=3, y =1
• x=-3, y =-1
• x=3 y=-1

What is the horizontal asymptote to this function?

• 4
• 0
• -2
• 1