Activity 13: Rational Functions & Limits Test Review

Where is the vertical asymptote in the graph of the function $f\left(x\right)=\frac{x-2}{x^2-4}$  

•  $x=4$  

•  $x=2$  

•  $x=-2$  

•  $x=-4$  

Tags

CCSS.HSF-IF.C.7D

Where is the horizontal asymptote located in the function?

 $\frac{4x^2+3x-2}{5x-7}$  

•  $y=0$  

• There is no horizontal asymptote

•  $y=\frac{4}{5}$  

•  $y=1$  

Tags

CCSS.HSF-IF.C.7D

Where is the hole located in the function? $f\left(x\right)=\frac{3x^2+14x-24}{x^2+5x-6}$  

•  $\left(-6,\ \frac{22}{7}\right)$  

•  $\left(-6,\ \frac{14}{5}\right)$  

•  $\left(6,\ \frac{22}{7}\right)$  

•  $\left(6,\ \frac{14}{5}\right)$  

Tags

CCSS.HSF-IF.C.7D

Where is the x-intercept located in the function? $f\left(x\right)=\frac{3x^2+14x-24}{x^2+5x-6}$  

•  $\frac{4}{3}$  

•  $-6$  

•  $-\frac{4}{3}$  

•  $6$  

Tags

CCSS.HSF-IF.C.7D

Where is the y-intercept located in the graph of the function $f\left(x\right)=\frac{x-2}{x^2-4}$  

•  $x=2$  

•  $x=\frac{1}{2}$  

•  $x=-\frac{1}{2}$  

•  $x=-2$  

Tags

CCSS.HSF-IF.C.7D

Find the value of the limit, if it exists. $\lim_{x\rightarrow6}\left(\frac{x^2-36}{x-6}\right)$  

• The limit does not exist

•  $\infty$  
  

• 6

• 12

 Find  $\lim_{x\rightarrow2^+\ }f\left(x\right)$  

•  $-1$  

•  $5$  
  

•  $0$  
  

• The limit does not exist

 Find  $\lim_{x\rightarrow-4\ }f\left(x\right)$  

•  $-2$  
  

•  $3$  
  

•  $-4$  
  

• The limit does not exist

Find the limit. $\lim_{x\rightarrow-\infty}\left(\frac{3x^5+21x^3}{7x^5-18x+4}\right)$  

•  $\frac{3}{7}$  

•  $0$  
  

•  $\infty$  
  

• The limit does not exist

Find the limit, if it exists. $\lim_{x\rightarrow\infty}\left(\frac{x^2-x-12}{x+3}\right)$  

•  $=1$  
  

•  $=0$  
  

•  $=2$  

• Limit Does Not Exist