Solving Polynomial and Rational Inequalities (and review)

Solve for x:
 $\frac{-x-6}{x+3}>0$  

•  $\left(-6,-3\right)$  

•  $\left[-6,\ -3\right)$  

•  $\left(-\infty,\ -6\right)\cup\left(-3,\ \infty\right)$  

•  $\left(-\infty,\ -6\right]\cup\left[-3,\ \infty\right)$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Assuming the scale is 1, where is f(x) < 0?

• $\left[-4,-1\right]\cup\left[2,\ \infty\right)$

• $\left(-4,-1\right)\cup\left(2,\ \infty\right)$

• $\left(-\infty,-4\right]\cup\left[-1,\ 2\right]$

• $\left(-\infty,-4\right)\cup\left(-1,\ 2\right)$

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Assuming the scale is 1, determine where f(x) ≤ 0.

• $\left(-\infty,2\right]\cup\left[2,4\right)$

• $\left(4,\ \infty\right)$

• $\left(-\infty,4\right]$

• $\left(-\infty,2\right)\cup\left(2,4\right)$

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.11

Solve for x:
 $x^2-x\le6$  

•  $\left(-2,3\right)$  

•  $\left[-2,3\right]$  

•  $\left(-\infty,-2\right)\cup\left(3,\ \infty\right)$  

•  $\left(-\infty,-2\right]\cup\left[3,\ \infty\right)$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

Solve for x:
 $2x^2+9x-5<0$  

•  $\left(-5,\ \frac{1}{2}\right)$  

•  $\left[-5,\ \frac{1}{2}\right]$  

•  $\left(-\infty,-5\right)\cup\left(\frac{1}{2},\ \infty\right)$  

•  $\left(-10,1\right)$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

Solve for x:
 $\frac{3x}{x+4}-1\ge0$  

•  $\left(-\infty,-4\right]\cup\left[2,\ \infty\right]$  

•  $\left(-4,\ 2\right]$  

•  $\left[-4,\ 2\right]$  

•  $\left(-\infty,-4\right)\cup\left[2,\ \infty\right)$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Which of the following rational functions has the three attributes: vertical asymptote at x = -3, horizontal asymptote at y = 0, and a zero at -1?

• $f\left(x\right)=\frac{\left(x+1\right)}{\left(x+3\right)^2}$

• $f\left(x\right)=\frac{\left(x+1\right)}{\left(x+3\right)^{ }}$

• $f\left(x\right)=\frac{\left(x+1\right)^2}{\left(x+3\right)}$

• $f\left(x\right)=\frac{\left(x-1\right)}{\left(x-3\right)^2}$

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

Which of the following functions has the given three attributes:

no vertical asymptote, a horizontal asymptote at y = 3, and a y-intercept at 5.

• $g\left(x\right)=\frac{3x^2+10}{x^2+5}$

• $g\left(x\right)=\frac{3x^2+5}{x^2}$

• $g\left(x\right)=\frac{3x^2+5}{x^2+1}$

• $g\left(x\right)=\frac{3x^2}{x-5}$

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

Solve for x:
 $\frac{3x-7}{x+2}>1$  

•  $\left(-2,\ \frac{9}{2}\right)$  

•  $\left(-\infty,-2\right)\cup\left(\frac{9}{2},\ \infty\right)$  

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

•  $\left(-2,\ \frac{7}{3}\right)$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve for x:
 $-2x^3+2x^2+4x<0$  

•  $\left(-1,\ 0\right)\cup\left(2,\ \infty\right)$  

•  $\left(-\infty,\ -1\right)\cup\left(0,\ 2\right)$  

•  $\left(2,\ \infty\right)$  

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

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1