Properties of Rational Functions

What is the vertical asymptote for

 $f\left(x\right)=\frac{1}{x+4}-5$  

• x = -4

• x = 4

• y = 5

• y = -5

What is the horizontal asymptote for

 $f\left(x\right)=\frac{-3}{x}+2$  

• x = -3

• x = 0

• y = 2

• y = -2

What information would help you determine the vertical asymptote? (Check all that apply)

• The value of x that makes the denominator equal to zero

• The "h" value

• The "k" value

• The range

• The domain

What is the vertical transformation from the parent function?

 $f\left(x\right)=\frac{1}{x+5}+3$  

(hint: right, left, up or down)

What is the domain of

 $f\left(x\right)=\frac{-1}{x-2}-4$  

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

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

•  $\left(-\infty,\ 4\right)\cup\left(4,\ \infty\right)$  

•  $\left(-\infty,-4\right)\cup\left(-4,\ \infty\right)$  

What is the range of

 $f\left(x\right)=\frac{1}{x}-1$  

•  $\left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

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

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

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

What are the transformations from the parent function?

 $f\left(x\right)=-2\cdot\left(\frac{1}{x-3}\right)$  
check all that apply

• Right 3

• Vertical Stretch

• Reflect x-axis

• Down 3

• Left 3

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 horizontal asymptote? 

• x = 2
• x = 7
• y = 2
• y = 7

Tags

CCSS.HSF-IF.C.7D

How is this function transformed from the parent function?

• Translated left and up
• Translated right and up
• Translated left and down
• Translated right and down

Tags

CCSS.HSF.BF.B.3