Free Printable Asymptotes

1.

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

2.

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

a)

vertical

b)

horizontal

c)

slant

d)

none

3.

Graph

a)

A

b)

B

c)

C

d)

D

4.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

5.

Which of these is NOT an asymptote on this graph?

a)

x=-3

b)

x=3

c)

y=2

d)

y=-3

6.

What is the equation of the horizontal asymptote of the given function?

a)

y = 2

b)

x = 1

c)

There isn't one

d)

y = 5

7.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

8.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

9.

Factor:

7x+49

a)

$7x\left(x+49\right)$

b)

$7\left(x+7\right)$

c)

$49\left(x+7\right)$

d)

$x\left(7+49\right)$

10.

Factor:
$5a^2-15$

a)

$5\left(a^2-15\right)$

b)

$5a\left(a-15\right)$

c)

$5\left(a^2-3\right)$

d)

$5a\left(a-3\right)$

11.

$12c^2-20a^2$

Factor:

a)

$2\left(6c^2-10a^2\right)$

b)

$4\left(3c^2-5a^2\right)$

c)

$2a^2c^2\left(6-10\right)$

d)

$4\left(ca\right)^2\left(3-5\right)$

12.

$64-40ab$

Factor:

a)

$4\left(16-10ab\right)$

b)

$4ab\left(16-10ab\right)$

c)

$8ab\left(8-5ab\right)$

d)

$8\left(8-5ab\right)$

13.

$36a^2+24a$

Factor:

a)

$12a\left(3a+2\right)$

b)

$a\left(36a+24\right)$

c)

$12\left(3a^2+2a\right)$

d)

$a^2\left(36+24a\right)$

14.

Factor:
$18x^4-12x^2$

a)

$6x^2\left(3x^2-2\right)$

b)

$x^2\left(18x^2-12\right)$

c)

$6\left(3x^2-2x^2\right)$

d)

$6x\left(2x^3-2x\right)$

15.

Factor:

12ab^3+20b

a)

$4ab\left(3b+5\right)$

b)

$b\left(12ab^2+20\right)$

c)

$4b\left(3ab^2+5\right)$

d)

$12b\left(ab^2+2\right)$

16.

$10x^2+5x$

a)

$5\left(2x^2+5\right)$

b)

$5x\left(2x+1\right)$

c)

$10x^2\left(1x+2x\right)$

d)

$5x^2\left(2x^2+1\right)$

17.

Factor:

14x-21x^2

a)

$7\left(2x-3x^2\right)$

b)

$x\left(14-21x^2\right)$

c)

$14x\left(1-2x\right)$

d)

$7x\left(2-3x\right)$

18.

Factor:
$81m+48mn$

a)

$3m\left(27+16n\right)$

b)

$m\left(81+48n\right)$

c)

$3\left(27+16n\right)$

d)

$mn\left(81+48n\right)$

19.

Factor:
$8ab-56a$

a)

$8a\left(b-7\right)$

b)

$8\left(ab-7a\right)$

c)

$a\left(8b-56\right)$

d)

$8ab\left(1-7b\right)$

20.

Factor:
$a^2b^2+a$

a)

$a^2\left(b^2+1\right)$

b)

$ab\left(ab+1\right)$

c)

$a\left(ab^2+1\right)$

d)

$a\left(b^2+1\right)$

21.

Factor:
$15xy+30x^2y^2$

a)

$xy\left(15+30xy\right)$

b)

$15\left(xy+2x^2y^2\right)$

c)

$15xy\left(1+2xy\right)$

d)

$5xy\left(3+6xy\right)$

22.

Factor:
$36ab^2-48a^2b$

a)

$a^2b^2\left(16a-38b\right)$

b)

$6ab\left(6b-8a\right)$

c)

$12ab\left(3a-4b\right)$

d)

$12ab\left(3b-4a\right)$

23.

Factor:
$x^3y^2+x^2y+x$

a)

$xy\left(x^2y+x+1\right)$

b)

$x\left(x^2y^2+xy+1\right)$

c)

$x\left(x^3y+x^2+1\right)$

d)

$y\left(x^3y+x^2+x\right)$

24.

Factor:

8m^2n^2-24mn^3+16mn

a)

$8\left(m^2n^2-3mn^3+2mn\right)$

b)

$8mn\left(mn-3mn+2mn\right)$

c)

$8mn\left(mn-3n^2+2\right)$

d)

$mn\left(8mn-24n^2+16\right)$

25.

Factor:

10x^3y^2-2xy^2+14xy

a)

$xy\left(10x^2y-2y+14\right)$

b)

$2xy\left(5x^2y-y+7\right)$

c)

$2xy\left(10x^2y-y+7\right)$

d)

$xy\left(5x^2y-y+7\right)$

26.

Factor:

9xz^3+18yz^2+24z^2

a)

$3z^2\left(3xz+6y+8\right)$

b)

$9z^2\left(xz+2y+3\right)$

c)

$3z\left(3xz^2+6yz+24z\right)$

d)

$9z\left(xz^2+2yz+3z\right)$

27.

Factor:

16x^6y+16x^2y^4+32x^3y^2

a)

$16x^2y\left(x^3+y^4+2xy\right)$

b)

$16xy\left(x^6+xy^3+2x^2y\right)$

c)

$16x^2y\left(x^4+y^3+2xy\right)$

d)

$16x^2y\left(x^4+y^3+2\right)$

28.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

29.

Factor:
x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

30.

Factor:
x² - 10x - 24

a)

(x + 12)(x - 2)

b)

(x - 6)(x - 4)

c)

(x - 12)(x + 2)

d)

(x +6)(x - 4)

31.

What are the factors of 3x²-17x+10

a)

(x-5)(3x-2)

b)

(x+5)(3x+2)

c)

(3x-5)(x-2)

d)

(x+5)(3x-2)

32.

What are the factors of x²+3x-40

a)

(x+10)(x-4)

b)

(x+8)(x-5)

c)

(x+20)(x-2)

d)

(x+1)(x-3)

33.

What are the factors of x²-8x-48

a)

(x-12)(x+4)

b)

(x+12)(x-4)

c)

(x+12)(x+4)

d)

(x-12)(x-4)

34.

Find the factors of x²-81

a)

(x-9)(x+9)

b)

(x+9)(x+9)

c)

(x-9)(x-9)

d)

Can't be factored

35.

Find the factors of 5x²+20x+20

a)

5(x+2)(x+2)

b)

5(x-2)(x-2)

c)

5(x+2)(x-2)

d)

(5x+2)(x+2)

36.

Find the factors of 4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

37.

Factor:
3x²-17x+10

a)

(x-5)(3x-2)

b)

(x+5)(3x+2)

c)

(3x-5)(x-2)

d)

(x+5)(3x-2)

38.

Factor:
4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

39.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

40.

x²+4x-32=0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

41.

x²-14x-51=0

a)

x= 17, -3

b)

x= -17, 3

c)

x= -17, -3

42.

3x²+9x-30=0

a)

x= 2, -5

b)

x= 5, -2

c)

x= -5, -2

43.

6x²-x-2=0

a)

x= -2/3, 1/2

b)

x= 2/3, -1/2

c)

x= -2/3, -1/2

44.

What are the factors AND solutions of x² + 2x – 3 = 0

a)

(x - 2)(x + 1); x=2, x=-1

b)

(x + 1)(x - 3); x=-1, x=3

c)

(x + 2)(x - 1); x=-2, x=1

d)

(x - 1)(x + 3); x=1, x=-3

45.

Solve by factoring:3x² + 5x + 2 = 0

a)

x = -2/3 and x = -1

b)

x = -3/2 and x = -1

c)

x = 2/3 and x = 1

d)

x = 2/3 and x = -1

46.

Solve by factoring: 2x²+ 7x + 6 = 0

a)

x= 3/2 and x = 2

b)

x = -3/2 and x = -2

c)

x = 6 and x = 7

d)

x = -6 and x = -7

47.

Solve by factoring: 4x² + 11x - 3 = 0

a)

x = -3/4 and x = -1

b)

x = 4 and x = 3

c)

x = 1/4 and x = -3

d)

x = -1/4 and x = 3

48.

Select all vertical asymptotes of the graph shown above.

a)

$x=0$

b)

$y=0$

c)

$y=1$

d)

$x=4$

49.

Identify the horizontal asymptote(s) from the graph.

a)

$x=-5$

b)

$x=2$

c)

$y=2$

d)

$y=0$

e)

$x=5$

50.

Identify the vertical asymptote from the graph.

a)

$x=-3$

b)

$y=-3$

c)

$x=3$

d)

$y=3$

51.

Identify the horizontal asymptote from the given graph.

a)

$x=-3$

b)

$y=-3$

c)

$x=3$

d)

$y=3$

52.

What are the equations of the asymptotes of the given graph

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x= -2, y = 1

c)

x=2 and y= -1

d)

x=1, y =2, y = -2

53.

Which of these is NOT an asymptote on this graph?

a)

x=-3

b)

x=3

c)

y=2

d)

y=-3

54.

What is the equation of the horizontal asymptote of the given function?

a)

y = 2

b)

x = 1

c)

There isn't one

d)

y = 5

55.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

56.

How did we transform from the parent function?
y = -1/5(x - 1)² + 7

a)

reflection, vertical compression, horizontal right, vertical up

b)

vertical compression, horizontal shift left, vertical shift up

c)

reflection, horizontal shift right, vertical shift down

d)

no changes were made to y = x²

57.

How did we transform from y=x^2?y = -3x²

a)

reflection and horizontal compression

b)

reflection and vertical stretch

c)

horizontal stretch

d)

reflection and vertical compression

58.

What is the vertex of the quadratic function: y=1/2 (x-3)²+8?

a)

(3,8)

b)

(-3,-8)

c)

(-3,8)

d)

(3,-8)

59.

Which equation has a vertex of (-3, 4)?

a)

y = 2(x+3)²+ 4

b)

y = (x+3)² - 4

c)

y = (x-3)² + 4

d)

y = 2(x - 3)² + 4

60.

In the equation f(x)=5(x+3)²-10 what does the 5 do?

a)

Vertical stretch by 5

b)

Horizontal compress by 5

c)

Reflect

d)

Move up 5

61.

Which quadratic function is represented by the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

62.

If the blue graph is
f(x) = x²
then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

63.

What transformations occurred to get f(x), the red graph, to become g(x), the blue graph?

a)

horizontal shift down and vertical shift left

b)

horizontal shift left and vertical shift down

c)

horizontal shift right and vertical shift up

d)

horizontal shift up and vertical shift right

64.

Does the graph of this equation open up or down?
f(x) = -(x + 3)² - 5

a)

up

b)

down

65.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

y intercept

66.

Does this graph have a maximum or minimum?

a)

Minimum

b)

Maximum

67.

What is the axis of symmetry for this graph?

a)

y=2

b)

x=2

c)

x=0

d)

y=0

68.

What is the vertical shift of this equation?
y = -(x + 3)² - 5

a)

left 5

b)

right 5

c)

up 5

d)

down 5

69.

What is the horizontal shift of this equation?
y = 3/4 (x - 5)² + 12

a)

up 5

b)

down 5

c)

left 5

d)

right 5

Asymptotes

Total questions: 69

Worksheet time: 52mins

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