Free Printable Unit 6 Review for Rational Functions TEST

1.

Simplify (6-1):

$\frac{x^2\ -\ 36}{x^2\ +\ 12x\ +\ 36}$

a)

$\frac{x\ -\ 6}{x\ +\ 6}$

b)

$\frac{x\ +\ 6}{x\ -\ 6}$

c)

$\frac{\left(x\ +\ 6\right)\left(x\ -\ 6\right)}{\left(x\ +\ 9\right)\left(x\ +\ 4\right)}$

d)

$\frac{x\ -\ 18}{x\ -\ 2}$

2.

Divide/simplify (6-2):
$\frac{\left(x\ +\ 5\right)\left(x\ -\ 2\right)}{\left(x\ +\ 6\right)\left(x\ -\ 6\right)}\div\frac{x^2\ -\ 25}{x^2\ +\ 3x\ -\ 18}$

a)

$\frac{\left(x\ +\ 5\right)\left(x\ -\ 2\right)}{\left(x\ +\ 6\right)\left(x\ -\ 6\right)}$

b)

$\frac{\left(x\ -\ 6\right)\left(x\ -\ 5\right)}{\left(x\ -\ 2\right)\left(x\ -\ 3\right)}$

c)

$\frac{x\ -\ 2}{x\ -\ 6}$

d)

$\frac{\left(x\ -\ 2\right)\left(x\ -\ 3\right)}{\left(x\ -\ 6\right)\left(x\ -\ 5\right)}$

3.

Add (6-3) $\frac{3}{x\ -\ 5}\ +\ \frac{8}{\left(x\ +\ 5\right)\left(x\ -\ 5\right)}$

a)

$\frac{-5}{\left(x\ +\ 5\right)\left(x\ -\ 5\right)}$

b)

$\frac{11}{\left(x\ +5\right)\left(x\ -\ 5\right)}$

c)

$\frac{3x\ +\ 23}{\left(x\ +\ 5\right)\left(x\ -\ 5\right)}$

d)

$\frac{3x\ +\ 8}{\left(x\ +\ 5\right)\left(x\ -\ 5\right)}$

4.

Solve for x. (6-5)

$\frac{x\ -\ 3}{x\ -\ 1}\ =\ \frac{x\ -\ 2}{x\ +\ 3}$

a)

$x\ =\ \frac{11}{3}$

b)

$x\ =\ \frac{-7}{3}$

c)

$x\ =\ \frac{7}{3}$

d)

$x\ =\ \frac{-11}{3}$

5.

Can x = -6 be solution to following equation? (6-5)

$\frac{4}{x\ +\ 6}\ +\ \frac{2}{5}\ =\ \frac{3}{x}$

a)

YES, x = -6 can be a solution

b)

NO, x =-6 can not be a solution

6.

Which rational function is graphed? (6-6)

a)

$y\ =\ \frac{1}{x\ +\ 5}\ +\ 2$

b)

$y\ =\ \frac{1}{x\ -\ 5}\ +\ 2$

c)

$y\ =\ \frac{1}{x\ -\ 2}\ +\ 5$

d)

$y\ =\ \frac{-1}{x\ +\ 5}\ -\ 2$

7.

Which rational function is graphed (6-6)?

a)

$y\ =\ \frac{1}{x\ +\ 3}\ -4$

b)

$y\ =\ \frac{-1}{x\ +\ 3}\ -\ 4$

c)

$y\ =\ \frac{-1}{x\ -\ 3}\ -\ 4$

d)

$y\ =\ \frac{-1}{x\ -\ 3}\ +\ 4$

8.

Find the Horizontal Asymptote (6-7)

$y\ =\frac{x^2\ -\ 2x\ -\ 3}{x^2\ +\ 3x\ +\ 2}$

a)

H.A. at $y\ =\ \frac{-3}{2}$

b)

H.A at $y\ =\ 2$

c)

H.A. at $y\ =\ 1$

d)

There is no H.A.

9.

Find the Holes (6-7)

$y\ =\frac{\left(x\ -\ 3\right)\left(x\ +\ 1\right)}{\left(x\ +\ 2\right)\left(x\ +\ 1\right)}$

a)

Hole at x = -1

b)

H.A at x = -2

c)

H.A. at x = 1

d)

There are no holes.

10.

Find the Vertical Asymptote (6-7)

$y\ =\frac{\left(x\ -\ 3\right)\left(x\ +\ 1\right)}{\left(x\ +\ 2\right)\left(x\ +\ 1\right)}$

a)

V.A. at x = -2

b)

V.A at x = -1

c)

V.A. at x = 3

d)

There is no V.A.

Unit 6 Review for Rational Functions TEST

Total questions: 10

Worksheet time: 3hrs 30mins

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