Precalc Rational Functions Review

Find the y-intercept:

 $f\left(x\right)=\frac{x^2-4}{x^2+6x+5}$  

• 1

• 2, -2

•  $-\frac{4}{5}$  

• -1, -5

• None

Find the x-intercept(s):

 $f\left(x\right)=\frac{x^2-4}{x^2+6x+5}$  

• 1

• 2, -2

•  $-\frac{4}{5}$  

• -1, -5

• None

Find any horizontal asymptote(s):

 $f\left(x\right)=\frac{x^2-4}{x^3-9x^2+8x}$  

• 0

• y = 1

• 2, -2

• y = 0

• 0, 8, 1

Find any vertical asymptote(s):

 $f\left(x\right)=\frac{x^2-4}{x^3-9x^2+8x}$  

• None

• y = 0, 8, 1

• x = 2, -2

• y = 1

• x = 0, 8, 1

Find any hole(s):

 $f\left(x\right)=\frac{3x^2-48}{x^2-3x-28}$  

• (-4, 0)

• (7, 3)

•  $\left(-4,\frac{24}{11}\right)$  
  

• (7, 0)

• None

Find any vertical asymptote(s):

 $f\left(x\right)=\frac{3x^2-48}{x^2-3x-28}$  

• 7

• x = -4, x = 7

•  $x=\frac{12}{7}$  

• x = 7

• x = 3

For

 $f\left(x\right)=\frac{6x^3-8x+1}{8x^3+7x}$  , 

as  $x\rightarrow-\infty,\ \ f\left(x\right)\rightarrow$  ________

•  $\infty$  

•  $-\infty$  

•  $\frac{3}{4}$  

•  $-\frac{3}{4}$  

•  I like turtles.

What is the horizontal asymptote?

• y=0
• y=1
• y=-1/9
• This graph does not have a horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Find the slant asymptote of the function.

• y = 3x - 12
• y = x + 5
• y = 3x - 5
• y = 3x - 7

Tags

CCSS.HSF-IF.C.7D

What do you know about the slant asymptote(s) of this function?

• It does not have an slant asymptote.
• It has a slant asymptote; you would find it by setting the numerator equal to 0. 
• It has an slant asymptote; you would find it by using division to divide the numerator by the denomenator. 
• It has an slant asymptote; you would find it by finding the values of x that make the denomenator zero. 

Tags

CCSS.HSF-IF.C.7D