Free Printable Rational Diagnostic Test

1.

The holes of a rational function occur when :

a)

my pencil pokes a hole in the paper I'm working on

b)

there is something left in the denominator

c)

the value of f(0)

d)

a factor in the denominator cancels with a factor in the numerator

2.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

slant

d)

none

3.

Who is this?

a)

Powerpuff Girls

b)

Powderpuff Girls

c)

Chemical X Girls

d)

Three Flying Girls

4.

Identify the vertical asymptotes (hint: factor the denominator)

a)

A

b)

B

c)

C

d)

D

5.

Which of the following functions does NOT have a vertical asymptote?

a)

(x+3) ∕(x²-5)

b)

x ∕ (x-3)²

c)

(x²-4) ∕ (x+2)

d)

-2 ∕ x

6.

The horizontal asymptote equals zero when:

a)

the exponents in the numerator and denominator are equal

b)

the exponents in the numerator are less than the denominator

c)

the exponents in the numerator are greater than the denominator

7.

Identify the horizontal asymptotes

a)

A

b)

B

c)

C

d)

D

8.

Identify the horizontal asymptotes

a)

A

b)

B

c)

C

d)

D

9.

What are the asymptotes?

a)

x=-2 and y=-1

b)

x=-2 and y=1

c)

x=2 and y=1

d)

x=2 and y = -1

10.

Snow fell in Newton twice in one day. The town received 3/8 inch of snow in the morning and another 1/2 inch of snow in the afternoon. How many total inches of snow fell in Newton on that day?

a)

1/8

b)

3/10

c)

5/8

d)

7/8

11.

Who is this?

a)

Odie

b)

Felix

c)

Stripes

d)

Garfield

12.

State the domain restrictions.

a)

x ≠ -2

b)

x ≠ 2, 1

c)

x ≠ 2, -1

d)

x ≠ -2, 2, 1

13.

Determine the domain

a)

A

b)

B

c)

C

d)

D

14.

Who is this?

a)

Jerry

b)

Tom

c)

Sylvester

d)

Garfield

15.

a)

All Real #s; x ≠ 1

b)

All Real #s; x = −1

c)

All Real #s; x ≠ -2

d)

x ≠ −2

16.

What is the domain and range?

a)

D : All real number x ≠ -3
R: All real number y≠ 1

b)

D : All real number x ≠ 1
R: All real number y≠ -3

c)

D : All real number x ≠ 3
R: All real number y≠ 1

d)

D : All real number x ≠ -1
R: All real number y≠ 3

17.

Which graph matches the rational expression?

a)

b)

c)

d)

18.

Who's that Pokemon?

a)

Vulpix

b)

Flareon

c)

Zorua

d)

Fennekin

19.

Factor
n²-13n+40

a)

(n-5)(n-8)

b)

(n+5)(n-8)

c)

(n-5)(n+8)

d)

(n+6)(n+1)

20.

Who's this?

a)

Magneto

b)

Flash

c)

QuickSilver

d)

Fast Guy

21.

Simplify

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

22.

Who's this?

a)

Starfire

b)

Blackfire

c)

Raven

d)

Cyborg

e)

Robin

23.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

24.

Who's this?

a)

Batman

b)

Superman

c)

Joker

d)

Lego Guy

25.

Simplify and state the excluded values.

a)

A

b)

B

c)

C

d)

D

26.

Who is this?

a)

Steven Universe

b)

Steven Galaxy

c)

Steven Planet

d)

Steven Earth

27.

Find the LCD of these fractions.

a)

3x

b)

9x

c)

x

d)

18x

28.

Who is this?

a)

Vegeta

b)

Gohan

c)

Bardock

d)

Goku

29.

Find the LCD of these fractions.

a)

x²

b)

2x

c)

2x²

d)

x

30.

Who's this?

a)

Dexter

b)

Hulk

c)

Krunk

d)

Valhallen

31.

Subtract the following rational expression.

a)

(28x-29) / 5(7x+6)

b)

(28x-11) / 5(7x+6)

c)

(7x-11) / 5(7x+6)

d)

(7x-29) / 5(7x+6)

32.

Who is this?

a)

Spongebob

b)

Gary

c)

Patrick

d)

Squidward

33.

Add

a)

A.

b)

B.

c)

C.

d)

D.

34.

Three friends shared a pizza. Mary ate 3/8 of the pizza, Jolene ate 3/16 of the pizza, and Susan ate 1/4 of the pizza. After they were finished eating, how much of the pizza was left?

a)

1/4

b)

3/16

c)

4/16

d)

1/2

35.

Who is this?

a)

Goku

b)

The Dragon

c)

Piccolo

d)

Yoshi

36.

Solve by cross-multiplying

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

37.

Who's this?

a)

Bukamon

b)

Gomamon

c)

Seel

d)

Joe

38.

Solve the equation for x.

a)

7

b)

6

c)

14

d)

0

39.

Who's this?

a)

QuickSilver

b)

Mr. Incredible

c)

Flash

d)

Daredevil

40.

Name the transformation.

a)

Translation

b)

Reflection

c)

Rotation

41.

Fence painting. Kiyoshi can paint a certain fence in 3 hours by himself. If Red helps, the job takes only 2 hours. How long would it take Red to pain the fence by himself?

a)

6 hours

b)

3 hours

c)

2 hours

d)

4 hours

42.

Who's this?

a)

Kirara

b)

Eevee

c)

Espeon

d)

Katrina

e)

Sango

43.

a)

x+5

b)

x+2

c)

x-10

d)

x-4

e)

x+6

44.

a)

$2x^2+3x+8-\frac{57}{x-4}$

b)

$2x^2-13x-56$

c)

$2x^2+3x+8+\frac{7}{x-4}$

d)

$2x^2-3x-16-\frac{89}{x-4}$

45.

Sheffert's Spooky Pumpking Patch models their sales as

N\left(t\right)=\frac{200t^2+20t+4}{t^2+1}

. Which of the following expressions is equivalent?

a)

$200\left(t^2+1\right)+20t-196$

b)

$200+\frac{20t-196}{t^2+1}$

c)

$\frac{200}{t^2+1}+20t-196$

46.

Who is this?

a)

Kuromi

b)

Hello Kitty

c)

My Melody

d)

Cinnamaroll

e)

Retsuko

47.

The absorbance varies directly with the concentration of an unknown substance, and the

absorbance is 0.3 when the concentration is 100 mg/dL. Find the concentration when the absorbance is 0.15.

a)

0.6 mg/dL

b)

50 mg/dL

c)

30 mg/dL

d)

0.45 mg/dL

48.

What is the value of x?

a)

4

b)

5

c)

10

d)

20

e)

100

49.

If the temperature is constant, the volume of gas varies inversely with the pressure. If the

pressure on 3 ft³ of gas is 15 lb/ft², what is the pressure when the volume is 4.5 ft³?

a)

22.5 lbs/ft²

b)

5 lbs/ft²

c)

10 lbs/ft²

50.

In an electronics store, 1/9 of the gadgets are cameras, and 1/5 of the remaining gadgets are gaming consoles. The rest are smartphones. If there are 180 gadgets, how many are smartphones?

a)

36

b)

32

c)

128

d)

144

Rational Diagnostic Test

Total questions: 50

Worksheet time: 1hrs 10mins

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