5.6pc MQ Rational Inequalities

Solve the rational inequality and state your solution in interval notation.


 $\frac{-x}{x-3}\ge0$  

•  $\left(0,\ +\infty\right)$  

•  $\left[0,\ 3\right)$  

•  $\left(-\infty,\ 0\right)\cup\left(3,\ +\infty\right)$  

•  $\left(-\infty,\ 0\right]\cup\left[3,\ +\infty\right)$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve the rational inequality and state your solution in interval notation.

 $\frac{3x-7}{x+2}>0$  

•  $\left(-2,\ \frac{7}{3}\right)$  

•  $\left(\ \frac{7}{3},\ +\infty\right)$  

•  $\left(-\infty,-2\right)\cup\left(\frac{7}{3},\ +\infty\right)$  

•  $\left(-\infty,-2\right)\cup\left[\frac{7}{3},\ +\infty\right)$  

Tags

CCSS.HSA.REI.B.3

Solve the rational inequality and state your solution in interval notation.


 $\frac{x-1}{x^2-4}<0$  

•  $\left(-\infty,\ -2\right)$ 

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

•  $\left(-\infty,\ -2\right)\cup\left(1,\ 2\right)$ 

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

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.4

Solve the rational inequality and state your solution in interval notation.

 $\frac{x^2-1}{x^2+1}\le0$  

•  $\left(-1,\ 1\right)$  

•  $\left[-1,\ 1\right]$  

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

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

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

Solve the rational inequality and state your solution in interval notation.


 $\frac{x^2+4x-12}{x^2-4x+4}>0$  

•  $\left(-\infty,\ -2\right]\cup\left[6,\ +\infty\right)$  

•  $\left(-\infty,\ -2\right)\cup\left(6,\ +\infty\right)$  

•  $\left(-\infty,\ -6\right]\cup\left[2,\ +\infty\right)$  

•  $\left(-\infty,\ -6\right)\cup\left(2,\ +\infty\right)$ 

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.4

 Solve the rational inequality and state your solution in interval notation.


 $\frac{9-x^2}{x+1}\le0$ 

•  $\left[-3,\ -1\right)\cup\left[3,+\infty\right)$  

•  $\left[-1,\ 0\right]\cup\left[3,+\infty\right)$  

•  $(-∞,-1)\cup(-1,\ 3)$  

•  $(-∞,-3)\cup(-3,3)$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.4

State all of the asymptotes for the corresponding rational function.

•  $x=-1,\ x=1$  

•  $y=-1,\ y=1$  

•  $x=-1,\ x=1,\ y=0$  

•  $y=-1,\ y=1,\ x=0$  

What is the domain in interval notation for the corresponding rational function.

•  $x=-1,\ x=1$  

•  $x\ne-1,\ x\ne1$  

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

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

Which equations below state the asymptotes for the graph of the rational function?
  $f(x)=\frac{x^2}{x^2-9}$  

Check all that apply.

•  $x=3$  

•  $x=-3$  

•  $x=9$  

•  $y=0$  

•  $y=1$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.REI.D.10

Which statements below describe the domain of the rational function. 
  $f(x)=\frac{x^3}{x^2-9}$  

Check all that apply.

•  $x\ne3$  

•  $x\ne\pm3$  

•  $\left(-\infty,\ 3\right)\cup\left(3,\ +\infty\right)$  

•  $\left(-\infty,\ -3\right)\cup\left(3,\ +\infty\right)$  

•  $\left(-\infty,\ -3\right)\cup\left(-3,3\right)\cup\left(3,\ +\infty\right)$  

Tags

CCSS.HSA.APR.D.7