Rational Functions Test Review

What are the vertical asymptotes for the graph of the rational function? $\frac{\left(x+3\right)\left(x-5\right)\left(x+7\right)}{\left(x+1\right)\left(x+4\right)}$  

• x = 1, x = 4

• x = –1, x = –4

• x = 3, x = –5, x = 7

• x = –3, x = 5, x = –7
  

Tags

CCSS.HSF-IF.C.7D

What are the vertical asymptotes for the graph of the rational function? $\frac{x+8}{x^2-9x+14}$  

• x = –2, x = –7

• x = 2, x = –7

• x = -8

• x = 2, x = 7

Tags

CCSS.HSF-IF.C.7D

Find the horizontal asymptote of the graph of  $y=\frac{3x^6-7x+9}{7x^2+7x+9}$  

• y = 2

• y =  $\frac{3}{7}$  

• y = 0

• No horizontal asymptote

Tags

CCSS.HSF-IF.C.7D

Find the horizontal asymptote of the graph of $y=\frac{-2x^2+3x+2}{2x^2+6+2}$   

• y =1

• y = -1

• y = 0

• No horizontal asymptote

Tags

CCSS.HSF-IF.C.7D

What is the product in simplest form? $\frac{y^2}{y-3}\cdot\frac{y^2-y-6}{y^2+y}$   

•  $\frac{y\left(y+2\right)}{y+1}$  
  

•  $\frac{y\left(y-2\right)}{y+1}$  
  

•  $\frac{y\left(y+2\right)}{y-1}$  

•  $\frac{y+2}{y+1}$  

Tags

CCSS.HSA.APR.D.7

What is the quotient in simplified form?

 $\frac{x^2-16}{x^2+5x+6}\div\frac{x^2+5x+4}{x^2-2x-8}$  

•  $\frac{\left(x-4\right)\left(x+4\right)}{\left(x+3\right)\left(x+1\right)}$  

•  $\frac{\left(x-4\right)\left(x+4\right)}{\left(x+3\right)\left(x+2\right)\left(x+1\right)}$  

•  $\frac{\left(x-4\right)\left(x-4\right)}{\left(x+3\right)\left(x+1\right)}$  

•  $\frac{\left(x-4\right)}{\left(x+1\right)}$  

Tags

CCSS.HSA.APR.D.6

Simplify the sum.

 $\frac{x^2+7x+10}{x^2+2x-15}+\frac{10}{x-3}$  

•  $\frac{x+12}{x-3}$  

•  $\frac{x+2}{x-3}$  

•  $\frac{x^2+7x+20}{x^2+2x-15}$  

•  $x+12$  

Tags

CCSS.HSA.APR.D.7

Simplify the difference.

 $\frac{n^2-10n+24}{n^2-13n+42}-\frac{9}{n-7}$  

•  $\frac{n-4}{n-7}$  

•  $n-13$  

•  $\frac{n-13}{n-7}$  

•  $\frac{n^2-10n+15}{n^2-13n+42}$  

Tags

CCSS.HSA.APR.D.7

Solve for x: $\frac{5}{x+2}=\frac{1}{x-4}$  

•  $x=5$  

•  $x=\frac{11}{2}$  

•  $x=4$  

•  $x=-4$  

Tags

CCSS.HSA.REI.A.2

 $\frac{r+7}{r^2+r}-1=\frac{r-1}{r}$  

•  $r=\frac{1}{2},-2$  

•  $r=2,-2$  

•  $r=\frac{1}{2},-6$  

•  $r=\frac{1}{2}$  

Tags

CCSS.HSA.REI.A.2