Unit 4 Review Rationals

Unit 4 Review

Multiple Choice

 $\frac{12}{x^2+5x-24}+\frac{3}{x-3}=\frac{Ax+B}{\left(x+8\right)\left(x-3\right)}$  

• A=3 
  
  B=12

• A=-3 
  
  B=36

• A=3
  B=-12

• A=3
  B=36

Multiple Choice

 $\frac{2x+4}{x^2-25}\cdot\frac{x^2-5x-50}{4x^2-16}$  

•  $\frac{x-10}{2\left(x-5\right)\left(x-2\right)}$  

•  $\frac{4x-20}{2\left(x-5\right)\left(x-2\right)}$  

•  $\frac{x-10}{4\left(x-5\right)\left(x-2\right)\left(x+2\right)}$  

•  $\frac{4x-20}{4\left(x-5\right)\left(x-2\right)\left(x+2\right)}$  

Multiple Choice

 $\frac{3x^2+13x+4}{x^2-4}\div\frac{4x+16}{x+2}$  

•  $\frac{x+4}{4\left(x-2\right)}$  

•  $\frac{3x+1}{4\left(x-2\right)}$  

•  $\frac{x+2}{4\left(x-2\right)}$  

•  $\frac{3x+4}{4\left(x-2\right)}$  

Multiple Choice

What are the restricted values of the expression?

 $\frac{x+4}{x^2-16}$  

• 16, -16

• 12, -12

• 4, -4

• 2, -2

Multiple Choice

Anne and Maria play tennis almost every weekend. So far, Anne has won 12 out of 20 matches. How many matches will Anne have to win in a row to improve her winning percentage to 75%

• 12

• 14

• 16

• 18

Multiple Choice

Working together, Bill and Tom painted a fence in 4 hours. If Tom has painted the same fence before by himself in 7 hours, how long (in hours) would it take Bill on his own?

• 0.1 hours

• 9.3 hours

• 2.5 hours

• 11 hours

Multiple Choice

What is the domain of the following function?

 $\frac{2x^2+2x-4}{x^2-5x-14}$  

• All real numbers

• All real numbers except x=2 and x=-2
   $\left(-\infty,\ -2\right)U\ \left(-2,\ 2\right)U\left(2,\ \infty\right)$  
  

• All real numbers except x=-2 and x=7
  
   $\left(-\infty,\ -2\right)U\left(-2,\ 7\right)U\left(7,\ \infty\right)$  
  

• All real numbers except x=-7
   $\left(-\infty,-7\right)U\left(-7,\ \infty\right)$  
  

Multiple Choice

Which expression has an horizontal asymptote of y=0?

• 
  

  $\frac{x^2+2x-7}{x-2}$
  

• $\frac{5x-7}{7x+5}$

• $\frac{3x^5+7x-1}{2x^7+3}$

• None of the above

Multiple Choice

What are all of the points of discontinuity in the expression?

 $\frac{2x\left(x+5\right)}{\left(3x+1\right)\left(x+5\right)}$  

•  $x=-\frac{1}{3}\ \left(VA\right),\ x=-5\ \left(Hole\right),\ y=\frac{2}{3}\left(HA\right)$  

•  $x=-5\ \left(VA\right),\ x=-\frac{1}{3}\ \left(Hole\right),\ y=\frac{2}{3}\left(HA\right)$  

•  $x=-5\ \left(VA\right),\ x=-\frac{1}{3}\ \left(Hole\right),\ No\ HA$  

•  $x=-\frac{1}{3}\ \left(VA\right),\ x=-5\ \left(Hole\right),\ y=0\left(HA\right)$  

Multiple Choice

What is the vertical asymptote?

• x=1

• x=2

• y=1

• y=2

Multiple Select

 $\frac{1}{2x+5}=\frac{x}{11x+8}$  Solve for x select all that apply.

• 1

• -1

• 4

• No Solution

Multiple Choice

What is the horizontal asymptote?

• x=1

• x=2

• y=1

• y=2