Properties of Rational Functions

What are the asymptotes?

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

Tags

CCSS.HSF-IF.C.7D

What is the vertical asymptote? 

• x = 2
• y = 2
• x = 1
• y = 1

Tags

CCSS.HSF-IF.C.7D

What is the range of the function?

•  $\left(-\infty,-1\right)\cup\left(-1,\infty\right)$  

•  $\left(-\infty,\ 1\right)\cup\left(1,\ \infty\right)$  
  

•  $\left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)$  
  

•  $\left(-\infty,-2\right)\cup\left(-2,\ \infty\right)$ 

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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

•  $x=0$  
   $x=3$  
  

•  $x=0$  
   $x=-3$  
  

•  $y=0$  
   $y=3$  
  

• There are no vertical asymptotes.  

Tags

CCSS.HSF-IF.C.7D

 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 the y-intercepts. 
 $y=\frac{x^2-1}{2x^2+8x+6}$  

•  $\left(1,\ 0\right)$   and  $\left(-1,\ 0\right)$  

•  $\left(0,\ 1\right)$   and  $\left(0,\ -1\right)$  

•  $\left(0,\ -\frac{1}{6}\right)$  

•  $\left(\frac{1}{6},\ 0\right)$  

Tags

CCSS.HSF-IF.C.7D

Identify the x-intercepts. 
 $y=\frac{x^2+2x-8}{-3x+3}$  

•  $\left(-4,\ 0\right)$   and  $\left(2,\ 0\right)$  

•  $\left(0,\ -4\right)$   and  $\left(0,\ 2\right)$  

•  $\left(0,\ -\frac{8}{3}\right)$  

•  $\left(-\frac{8}{3},\ 0\right)$  

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

Find the y-intercept.

• (0, -2)

• (0, 2)

• (0, 4)

• it is undefined

What is the horizontal asymptote of this function?

• y=2
• x=1/2
• y=1
• y=1/2

Tags

CCSS.HSF-IF.C.7D