Free Printable Asymptotes of Rational Functions

1.

What feature is being calculated here?

a)

x-intercepts

b)

y-intercept

c)

Vertical Asymptote

d)

Horizontall Asymptote

e)

Oblique Asymptote

2.

What feature is being calculated here?

a)

x-intercepts

b)

y-intercept

c)

Vertical Asymptote

d)

Horizontal Asymptote

e)

Oblique Asymptote

3.

If you're trying to find the Vertical Asymptotes of a rational function that is written in Standard Form, what do you need to do first?

a)

Factor it and Simplify

b)

Do Limits

c)

Do Polynomial Long Division

d)

Plug in 0 for x

e)

Plug in 0 for y

4.

What are the x-int (s) of this function?

Select all that apply

f\left(x\right)=\frac{3\left(x-5\right)\left(2x+3\right)}{\left(x-5\right)\left(7x-2\right)}

a)

( 5 , 0 )

b)

( -3 , 0 )

c)

( 3.5 , 0 )

d)

( 2 , 0 )

e)

( - 1.5 , 0 )

5.

How do you calculate x-int (s) ?

a)

Plug zero in for y or f(x) and solve

b)

Plug zero into all the x's and evaluate

c)

Set the Denominator equal to zero and solve

d)

Use Limits

e)

Use Polynomial Long Division

6.

How do you calculate a y-int ?

a)

Plug zero in for y or f(x) and solve

b)

Plug zero into all the x's and evaluate

c)

Set the Denominator equal to zero and solve

d)

Set the Numerator equal to zero and solve

e)

Use Polynomial Long Division / Limits

7.

How do you calculate

Vertical Asymptotes ?

a)

Plug zero in for y or f(x) and solve

b)

Plug zero into all the x's and evaluate

c)

Set the Denominator equal to zero and solve

d)

Set the Numerator equal to zero and solve

e)

Use Polynomial Long Division / Limits

8.

Select all the ways you can calculate

Horizontal Asymptotes

a)

Plug zero in for y or f(x) and solve

b)

Plug zero into all the x's and evaluate

c)

Set the Denominator equal to zero and solve

d)

Use Limits

e)

Use Polynomial Long Division

9.

What is the only way to actually calculate

Oblique Asymptotes ?

a)

Plug zero in for y or f(x) and solve

b)

Plug zero into all the x's and evaluate

c)

Set the Denominator equal to zero and solve

d)

Use Limits

e)

Use Polynomial Long Division

10.

Which form should you use to find the

x-ints of a Rational Function?

a)

Standard Form

b)

Unsimplified Factored Form

c)

Simplified Factored Form

d)

Vertex / Graphing Form

e)

Rational Form

11.

Which form should you use to find the

y-int of a Rational Function?

a)

Standard Form

b)

Unsimplified Factored Form

c)

Simplified Factored Form

d)

Vertex / Graphing Form

e)

Rational Form

12.

Which form should you use to find the

Vertical Asymptotes of a Rational Function?

a)

Standard Form

b)

Unsimplified Factored Form

c)

Simplified Factored Form

d)

Vertex / Graphing Form

e)

Rational Form

13.

Which form should you use to find the

Horizontal Asymptotes of a Rational Function?

a)

Standard Form

b)

Unsimplified Factored Form

c)

Simplified Factored Form

d)

Vertex / Graphing Form

e)

Rational Form

14.

Which form should you use to find the

Oblique Asymptotes of a Rational Function?

a)

Standard Form

b)

Unsimplified Factored Form

c)

Simplified Factored Form

d)

Vertex / Graphing Form

e)

Rational Form

15.

A Rational Function will touch its

Vertical Asymptote (s) . . .

a)

Always

b)

Sometimes

c)

Never

16.

A Rational Function will touch its

Horizontal Asymptote . . .

a)

Always

b)

Sometimes

c)

Never

17.

When doing Polynomial Long Division, where do you put the Numerator?

a)

Inside the division box

b)

Outside the division box

c)

On top of the division box

d)

Under the division box

e)

In a USPS mail box

18.

When doing Polynomial Long Division, where do you put the Denominator?

a)

Inside the division box

b)

Outside the division box

c)

On top of the division box

d)

Under the division box

e)

In a lunch box

19.

What feature is this?

a)

Horizontal Asymptote

b)

Vertical Asmyptote

c)

Oblique Asymptote

d)

x - intercept

e)

y - intercept

20.

What feature is this?

a)

Horizontal Asymptote

b)

Vertical Asmyptote

c)

Oblique Asymptote

d)

x - intercept

e)

y - intercept

21.

What feature is this?

a)

Horizontal Asymptote

b)

Vertical Asmyptote

c)

Oblique Asymptote

d)

x - intercept

e)

y - intercept

22.

What feature is this?

a)

Horizontal Asymptote

b)

Vertical Asmyptote

c)

Oblique Asymptote

d)

x - intercept

e)

y - intercept

23.

What feature is this?

a)

Horizontal Asymptote

b)

Vertical Asmyptote

c)

Oblique Asymptote

d)

x - intercept

e)

y - intercept

24.

What feature is this?

Select all that apply

a)

Horizontal Asymptote

b)

Vertical Asmyptote

c)

Oblique Asymptote

d)

x - intercept

e)

y - intercept

25.

Which choice is the best way to label this feature?

a)

$y\ =-2x+4$

b)

$y=2x+4$

c)

$y=2x-4$

d)

$y=-2x-4$

e)

$y=-4$

26.

Which choice is the best way to label this feature?

a)

$y\ =-2x+4$

b)

$y=2x+4$

c)

$y=2x-4$

d)

$y=-2x-4$

e)

$y=-4$

27.

Which choice is the best way to label this feature?

a)

$y\ =-2x-4$

b)

$y=2x-4$

c)

$y=-2x$

d)

$x=-4$

e)

$y=-4$

28.

Which choice is the best way to label this feature?

a)

$y\ =-2x+4$

b)

$y=2x+4$

c)

$y=2x$

d)

$x=4$

e)

$y=4$

29.

What are the y-int (s) of this function?

Select all the apply

f\left(x\right)=\frac{4x^5\left(x+9\right)}{x^2\left(x-3\right)}

a)

( 0 , -12 )

b)

( 0 , -9 )

c)

Undefined - None

d)

( 0 , 0 )

e)

( 0 , 3 )

30.

What are the x-int (s) of this function?

Select all that apply

f\left(x\right)=\frac{4x^5\left(x+9\right)}{x^2\left(x-3\right)}

a)

( -12 , 0 )

b)

( -9 , 0 )

c)

Undefined - None

d)

( 0 , 0 )

e)

( 3 , 0 )

31.

What are the Vertical Asymptote (s) of this function? Select all that apply

f\left(x\right)=\frac{4x^5\left(x+9\right)}{x^2\left(x-3\right)}

a)

x = -12

b)

x = -9

c)

Undefined - None

d)

x = 0

e)

x = 3

32.

What are the y-int (s) of this function?

Select all that apply

f\left(x\right)=\frac{\left(x-8\right)\left(2x+5\right)}{\left(x+1\right)\left(x-4\right)}

a)

( 0 , 10 )

b)

( 0 , 8 )

c)

( 0 , 4 )

d)

( 0 , -2.5 )

e)

( 0 , -1 )

33.

What are the x-int (s) of this function?

Select all that apply

f\left(x\right)=\frac{\left(x-8\right)\left(2x+5\right)}{\left(x+1\right)\left(x-4\right)}

a)

( 10 , 0 )

b)

( 8 , 0 )

c)

( 4 , 0 )

d)

( -2.5 , 0 )

e)

( -1 , 0 )

34.

What are the Vertical Asymptote (s) of this function? Select all that apply

f\left(x\right)=\frac{\left(x-8\right)\left(2x+5\right)}{\left(x+1\right)\left(x-4\right)}

a)

x = 10

b)

x = 8

c)

x = 4

d)

x = -2.5

e)

x = -1

35.

What is the Horizontal Asymptote of this function?

f\left(x\right)=\frac{\left(x-8\right)\left(2x+5\right)}{\left(x+1\right)\left(x-4\right)}

a)

y = 2

b)

y = 0

c)

y = 4

d)

y = -2x - 5

e)

y = 1

36.

What is the Horizontal Asymptote of this function?

f\left(x\right)=\frac{8\left(x-2\right)\left(x+3\right)}{4\left(x+1\right)}

a)

y = 2

b)

y = 0

c)

y = 0.5

d)

No Horizontal Asymptote. Need to find Oblique Asymptote

e)

y = -1

37.

What is the Horizontal Asymptote of this function?

f\left(x\right)=\frac{x^3+7x^{2\ }+12x}{2x^4+10x^3}

a)

y = 2

b)

y = 0

c)

y = 0.5

d)

No Horizontal Asymptote. It's an Oblique Asymptote

e)

y = 1.583

38.

What is the Horizontal Asymptote of this function?

f\left(x\right)=\frac{x^4+7x^{3\ }+12x^2}{2x^3+10x^2}

a)

y = 2

b)

y = 0

c)

y = 0.5

d)

No Horizontal Asymptote. It's an Oblique Asymptote

e)

y = 1.583

39.

What is the Horizontal Asymptote of this function?

f\left(x\right)=\frac{8x^2-24x}{2x^2+2x-4}

a)

y = 4

b)

y = 0

c)

y = 0.25

d)

No Horizontal Asymptote. There's an Oblique Asymptote

e)

There's only Vertical Asymptotes

40.

$\frac{\infty}{10}$

What does this essentially equal?

a)

0

b)

Undefined

c)

$\infty$

d)

10

e)

5,400,650

41.

$\frac{10}{\infty}$

What does this essentially equal?

a)

0

b)

Undefined

c)

$\infty$

d)

10

e)

1

42.

To find Vertical Asymptotes of a Rational Function, why do we set the denominator equal to zero & solve?

a)

Because it tells you the inputs that will make the outputs undefined

b)

Because it tells you the inputs that will make the outputs 0

c)

You don't. That's not how you find the Vertical Asymptote(s)

43.

What does it mean to be a Vertical Asymptote?

Select all the apply

a)

It means that input makes its output undefined

b)

It means that input makes the denominator 0

c)

It means that input makes its output 0

d)

It means that input makes the numerator 0

e)

It means its equation looks like " y = "

44.

What is the Horizontal or Oblique Asymptote?

* Write your equations with a variable (x or y) , = , and NO spaces

(a)

45.

What is the Horizontal or Oblique Asymptote?

* Write your equations with a variable (x or y) , = , and NO spaces

(a)

46.

What feature is being calculated here?

a)

x - intercepts

b)

y - intercepts

c)

Vertical Asymptotes

d)

Horizontal Asymptotes

e)

Oblique Asymptotes

47.

What feature is being calculated here?

a)

x - intercepts

b)

y - intercepts

c)

Vertical Asymptotes

d)

Horizontal Asymptotes

e)

Oblique Asymptotes

48.

What's the error, if any?

a)

The numerator and denominator are in the wrong spots

b)

Didn't SUBTRACT the polynomial correctly

c)

Didn't MULTIPLY the polynomial correctly

d)

No error. This is correct.

e)

Don't stop, you have to keep going

49.

What's the error, if any?

a)

The numerator and denominator are in the wrong spots

b)

Didn't SUBTRACT the polynomial correctly

c)

Didn't MULTIPLY the polynomial correctly

d)

No error. This is correct.

e)

Don't stop, you have to keep going

50.

What feature is being calculated here?

a)

x - intercepts

b)

y - intercepts

c)

Vertical Asymptotes

d)

Horizontal Asymptotes

e)

Oblique Asymptotes

51.

What feature is being calculated here?

a)

x - intercepts

b)

y - intercepts

c)

Vertical Asymptotes

d)

Horizontal Asymptotes

e)

Oblique Asymptotes

Asymptotes of Rational Functions

Total questions: 51

Worksheet time: 27mins

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