Free Printable Rational Inequalities & key Features

1.

a)

(-2, 1)

b)

(-oo, -2) u (1,2)

c)

(1,2) u (2, oo)

d)

(-oo, -2] u [1,2]

2.

a)

[-1, 1]

b)

(-oo, -1) u (1, oo)

c)

(-1, 1)

d)

[1, oo)

3.

a)

(-oo, -4) u (3, oo)

b)

(-4, 3)

c)

[-4, 3]

d)

(-oo, -4] u [3, oo)

4.

a)

(-2,2)

b)

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

c)

[-2,2]

d)

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

5.

Solve for x:
$\frac{3x-7}{x+2}>1$

a)

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

b)

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

c)

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

d)

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

6.

a)

(0, 1)

b)

[-1, 0] u [1, oo)

c)

[0,1]

d)

(-1, 0) u (1, oo)

7.

a)

[0, 2]

b)

(-oo, 0) u (2, oo)

c)

(3, 4) u (-4, oo)

d)

(0, 2)

8.

a)

(-2,2)

b)

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

c)

[-2,2]

d)

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

9.

a)

$\left[0,3\right)$

b)

$\left(0,3\right]$

c)

$\left(-\infty,3\right]$

d)

$\left(-\infty,0\right)$

10.

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

$\frac{x^2+4x-12}{x^2-4x+4}>0$

a)

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

b)

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

c)

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

d)

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

11.

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

$\frac{9-x^2}{x+1}\le0$

a)

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

b)

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

c)

$(-∞,-1)\cup(-1,\ 3)$

d)

$(-∞,-3)\cup(-3,3)$

12.

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.

a)

$x=3$

b)

$x=-3$

c)

$x=9$

d)

$y=0$

e)

$y=1$

13.

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

Check all that apply.

a)

$x\ne3$

b)

$x\ne\pm3$

c)

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

d)

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

e)

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

14.

What are the x-intercepts for the rational function?
$f\left(x\right)=\frac{x^2-2x-8}{3x-2}$

a)

$\left(\frac{2}{3},\ 0\right)$

b)

$\left(-\frac{2}{3},\ 0\right)$

c)

$\left(-4,\ 0\ \right)\ \left(2,\ 0\right)$

d)

$\left(4,\ 0\ \right)\ \left(-2,\ 0\right)$

15.

$\frac{x+4}{x-3}$

For which value is the expression undefined?

a)

-4

b)

-3

c)

3

d)

0

16.

$\frac{-9x}{x+12}<-5$

a)

-12 < x < 15

b)

x > -12 or x > 15

c)

x < -12 or x > 15

d)

-12 > x > 15

17.

Solve for x:
$\frac{-x-6}{x+3}>0$

a)

$-6<x<-3$ $\$

b)

$-6\le x<-3$ $\$

c)

$x<-6\ or\ x>-3$

d)

$x<-6\ or\ x\ge-3$

18.

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?

a)

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

b)

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

c)

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

d)

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

19.

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.

a)

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

b)

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

c)

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

d)

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

20.

Graph the function
State the interval(s) of increase. $f\left(x\right)=\frac{x^2-1}{x^2-4x-5}$

a)

The function is always decreasing; therefore, there are no intervals of increase.

b)

$\left(-\infty,\ 5\right)$

c)

$\left(5,\ \infty\right)$

d)

$\left(-\infty,\ \infty\right)$

Rational Inequalities & key Features

Total questions: 20

Worksheet time: 19mins

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