Free Printable Review for Module 5 test Rational functions

1.

What is the Domain of this function?

a)

$\left[-6,\ 6\right]$

b)

$\left[0,\ 7\right]$

c)

$\left[2,\ 7\right]$

d)

No Solution

2.

What is the Range of this function?

a)

$\left[0,\ 7\right]$

b)

$\left[0,\ 6\right]$

c)

$\left[-6,\ 6\right]$

d)

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

3.

Add

$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$

a)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ \frac{1}{4}$

b)

$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ 1$

c)

$\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ \frac{1}{4}$

d)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-\frac{1}{4},\ 2$

4.

$\frac{x^2+4x-5}{x-3}\times\frac{x-3}{10x+50}$

Simplify.

a)

$\frac{x-2}{\left(x-6\right)\left(x+8\right)}$

b)

$\frac{4}{x+7}$

c)

$x\left(x-4\right)$

d)

$\frac{x-1}{10}$

5.

Solve

\frac{x}{2x-3}=\frac{3x}{x+11}

a)

x = 0 , 4

b)

x = 1 , 3

c)

x = -4 , 0

d)

x = 5 , 2

6.

$\frac{2}{x-2}-\frac{1}{x+1}=\frac{2}{x^2-x-2}$ Solve;

a)

x = 2

b)

x = -2

c)

x = 6

d)

x = 3

7.

How do you know if a factor in the denominator is a hole instead of a Vertical asymptote ?

a)

It cancels out

b)

it equals 0

c)

you set the numerator equal to 0

d)

you compare the degrees

8.

How do you find the y-intercept?

a)

replace all x-values with 0

b)

replace all y-values with 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

9.

How do you determine the Horizontal Asymptote?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

10.

A vertical asymptote is found by setting the _________= to zero and solving for x

a)

Numerator

b)

Denominator

c)

Right side

d)

Left side

11.

How do you find the x-intercept?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

12.

List the x value for the resulting hole in the graph? $f\left(x\right)=\frac{x^2-4}{x^2-5x+6}$

a)

2

b)

2 and 3

c)

-3

d)

3

13.

What are the vertical asymptote/s ?
$y=\frac{x^2-4}{x^2-5x+6}$

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

14.

What is the horizontal asymptote of this function?

y=\frac{x}{2x-6}

a)

y=2

b)

x=1/2

c)

y=1

d)

y=1/2

15.

Find the zeros, if one exists.

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

a)

$x=1$

b)

$x=-1$

c)

$x=-1,\ x=1$

d)

None

16.

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

What is the equation of the slant asymptote?

a)

y = x + 1

b)

y = x + 2

c)

y = x + 3

d)

y = x

17.

Graph the function.

$f\left(x\right)=\frac{-x+1}{x-4}$

a)

b)

c)

d)

18.

Which one should be used in the partial fraction decomposition of $\frac{x-11}{\left(x+3\right)^2\left(x-4\right)}?$

a)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)}+\frac{C}{\left(x-4\right)}$

b)

$\frac{A}{\left(x-4\right)}+\frac{Bx+C}{\left(x+3\right)^2}$

c)

$\frac{A}{\left(x+3\right)^2}+\frac{B}{\left(x-4\right)}$

d)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)^2}+\frac{C}{\left(x-4\right)}$

Review for Module 5 test Rational functions

Total questions: 18

Worksheet time: 30mins

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