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Worksheets

Transformations

Total questions: 100

Worksheet time: 1hrs 26mins

Name
Class
Date
1.

If point H(–6, 2) is translated 4 units up and 3 units right, what are the coordinates of the translated image?

a)

(-2, 5)

b)

(-3, 6)

c)

(-9, -2)

d)

(-9, 6)

2.

If point H(–6, 2) is translated 4 units up and 3 units right, what are the coordinates of the translated image?

a)

(-2, 5)

b)

(-3, 6)

c)

(-9, -2)

d)

(-9, 6)

3.

Point N(6, –5) is reflected across the

x-axis. What are the coordinates of the image?

a)

(-6, -5)

b)

(-5, 6)

c)

(5, -6)

d)

(6, 5)

4.

Suppose triangle RST shown on the

coordinate grid is reflected across the y-axis. Which ordered pair does not represent a vertex of the reflected triangle?

a)

(5, 1)

b)

(-4, -2)

c)

(2, -4)

d)

(-2, 4)

5.

Triangle LMN has vertices L(–1, 4), M(–2, 4), and N(–1, –1). What are the coordinates of the image of point M after a dilation with a scale factor of 3?

a)

(-6, 12)

b)

(-6, 4)

c)

(-2, 12)

d)

(12, -6)

6.

If the figure is rotated 90 degrees clockwise, what are the coordinates of R?

a)

(-3, 3)

b)

(3, -3)

c)

(-3, -3)

d)

(3, 3)

7.

Triangle RST has vertices R(–1, 1), S(3, 1), and T(3, –4). What are the coordinates of the image of RST after a translation 4 units to the left and 2 units down?

a)

R'(–5, 1), S'(–1, 1), and T'(–1, –4)

b)

R'(–5, –1), S'(3, –1), and T'(–1, –4)

c)

R'(–1, –1), S'(3, –1), and T'(3, –6)

d)

R'(–5, –1), S'(–1, –1), and T'(–1, –6)

8.

Point A(3, 5) was dilated, and the point after dilation was A’(6, 10).  What was the scale factor used?

a)

1/2

b)

2

c)

1

d)

3

9.

What scale factor was used for the dilation shown?

a)

1/2

b)

1

c)

2

d)

3

10.

The vertices of triangle GHI are G(1, 2), H(3, 4), and I(4, 2). The triangle will be reflected across the x-axis. What will be the coordinates of the image point H′?

a)

(-3, 4)

b)

(3, -4)

c)

(-3, -4)

d)

(3, 4)

11.

Point W is located at (7, 3) on a coordinate plane. Point W is translated 2 units to the left and 3 units up. What are the coordinates of the image point W′?

a)

(10, 1)

b)

(9, 0)

c)

(5, 6)

d)

(4, 1)

12.
Determine how to translate triangle A'B'C' to triangle ABC.
a)
(x+2, y-5)
b)
(x+2, y-9)
c)
(x-2, y-9)
d)

(x-2, y+9)

13.
Determine where X' would be if you translated X 3 units to the left and 9 units down.
a)
(-4, 4)
b)
(-10, 2)
c)
(-4, -5)
d)
(-1, 5)
14.
How was B translated to B' if B' is at (4, -2)?
a)
Translated 6 units down
b)
Translated 2 units to the left and 6 units down
c)
Translated 2 units to the right and 6 units down
d)
Translated 2 units to the right
15.
How is trapezoid ABCD translated to trapezoid A'B'C'D'?
a)
Translated 5 units down and 5 units to the right
b)
Translated 5 units down and 1 to the right
c)
Translated 8 units down and 5 units to the right
d)
Translated 5 units down and 4 units to the right
16.
Identify the transformation.
a)
Reflection across y axis
b)
Reflection across x-axis
c)
180 Rotation
d)
Translation 2 units down
17.

Describe the transformation:

(x, y) -> (x+3, y)

a)

Translation 3 units to the left

b)

Translation 3 units up

c)

Translation 3 units to the right

d)

Translation 3 units down

18.

Describe the transformation:

(x, y) -> (x, y-2)

a)

Translation 2 units to the left

b)

Translation 2 units up

c)

Translation 2 units to the right

d)

Translation 2 units down

19.

Describe the transformation:

(x, y) -> (x-2, y+7)

a)

Translation 2 units to the left & 7 units up

b)

Translation 2 units to the left & 7 units down

c)

Translation 2 units to the right & 7 units up

d)

Translation 2 units to the right & 7 units down

20.

Describe the transformation:

(x, y) -> (x-1, y+1)

a)

Translation 1 unit to the left & 1 unit down

b)

Translation 1 unit to the left & 1 unit up

c)

Translation 1 unit to the right & 1 unit down

d)

Translation 1 unit to the right & 1 unit up

21.

Describe the transformation:

(x, y) -> (x, y-10)

a)

Translation 10 units to the left

b)

Translation 10 units up

c)

Translation 10 units to the right

d)

Translation 10 units down

22.

Describe the transformation:

(x, y) -> (x, -y)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

23.

Describe the transformation:

(x, y) -> (-x, y)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

24.

Describe the transformation:

(x, y) -> (-y, x)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

25.

Describe the transformation:

(x, y) -> (y, -x)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

26.

Describe the transformation:

(x, y) -> (3x, y)

a)

Horizontal translations 3 units to the right

b)

Vertical translation 3 units up

c)

Horizontal stretch 3 times as wide

d)

Vertical stretch 3 times as tall

27.

Describe the transformation:

(x, y) -> (x, 2y)

a)

Horizontal translations 2 units to the right

b)

Vertical translation 2 units up

c)

Horizontal stretch 2 times as wide

d)

Vertical stretch 2 times as tall

28.

A mirror image of a figure

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

29.

to slide or move a figure

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

30.

Turning around a point

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

31.

To change the size of a figure

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

32.

What does it mean if two figures are congruent?

a)

The figures are the same shape, but different size

b)

The figures are different size and shape

c)

The figures are the same size and shape

d)

The figures are the same size, but different shape

33.

Are the figures congruent?

(What type of transformation is shown?)

a)

Congruent (rotation)

b)

Congruent (reflection)

c)

NOT Congruent (rotation)

d)

NOT Congruent (reflection)

34.

Are the figures congruent?

(What type of transformation is shown?)

a)

Congruent (rotation)

b)

Congruent (reflection)

c)

NOT Congruent (rotation)

d)

NOT Congruent (reflection)

35.

Are the figures congruent?

(What type of transformation is shown?)

a)

NOT Congruent (dilation)

b)

NOT Congruent (translation)

c)

Congruent (dilation)

d)

Congruent (translation)

36.

Are the figures congruent?

(What type of transformation is shown?)

a)

NOT Congruent (dilation)

b)

NOT Congruent (translation)

c)

Congruent (dilation)

d)

Congruent (translation)

37.

If point H(–6, 2) is translated 4 units up and 3 units right, what are the coordinates of the translated image?

a)

(-2, 5)

b)

(-3, 6)

c)

(-9, -2)

d)

(-9, 6)

38.

Point N(6, –5) is reflected across the

x-axis. What are the coordinates of the image?

a)

(-6, -5)

b)

(-5, 6)

c)

(5, -6)

d)

(6, 5)

39.

Suppose triangle RST shown on the

coordinate grid is reflected across the y-axis. Which ordered pair does not represent a vertex of the reflected triangle?

a)

(5, 1)

b)

(-4, -2)

c)

(2, -4)

d)

(-2, 4)

40.

Triangle LMN has vertices L(–1, 4), M(–2, 4), and N(–1, –1). What are the coordinates of the image of point M after a dilation with a scale factor of 3?

a)

(-6, 12)

b)

(-6, 4)

c)

(-2, 12)

d)

(12, -6)

41.

If the figure is rotated 90 degrees clockwise, what are the coordinates of R?

a)

(-3, 3)

b)

(3, -3)

c)

(-3, -3)

d)

(3, 3)

42.

Triangle RST has vertices R(–1, 1), S(3, 1), and T(3, –4). What are the coordinates of the image of RST after a translation 4 units to the left and 2 units down?

a)

R'(–5, 1), S'(–1, 1), and T'(–1, –4)

b)

R'(–5, –1), S'(3, –1), and T'(–1, –4)

c)

R'(–1, –1), S'(3, –1), and T'(3, –6)

d)

R'(–5, –1), S'(–1, –1), and T'(–1, –6)

43.

Point A(3, 5) was dilated, and the point after dilation was A’(6, 10).  What was the scale factor used?

a)

1/2

b)

2

c)

1

d)

3

44.

What scale factor was used for the dilation shown?

a)

1/2

b)

1

c)

2

d)

3

45.

The vertices of triangle GHI are G(1, 2), H(3, 4), and I(4, 2). The triangle will be reflected across the x-axis. What will be the coordinates of the image point H′?

a)

(-3, 4)

b)

(3, -4)

c)

(-3, -4)

d)

(3, 4)

46.

Point W is located at (7, 3) on a coordinate plane. Point W is translated 2 units to the left and 3 units up. What are the coordinates of the image point W′?

a)

(10, 1)

b)

(9, 0)

c)

(5, 6)

d)

(4, 1)

47.
Determine how to translate triangle A'B'C' to triangle ABC.
a)
(x+2, y-5)
b)
(x+2, y-9)
c)
(x-2, y-9)
d)

(x-2, y+9)

48.
Determine where X' would be if you translated X 3 units to the left and 9 units down.
a)
(-4, 4)
b)
(-10, 2)
c)
(-4, -5)
d)
(-1, 5)
49.
How was B translated to B' if B' is at (4, -2)?
a)
Translated 6 units down
b)
Translated 2 units to the left and 6 units down
c)
Translated 2 units to the right and 6 units down
d)
Translated 2 units to the right
50.
How is trapezoid ABCD translated to trapezoid A'B'C'D'?
a)
Translated 5 units down and 5 units to the right
b)
Translated 5 units down and 1 to the right
c)
Translated 8 units down and 5 units to the right
d)
Translated 5 units down and 4 units to the right
51.
Identify the transformation.
a)
Reflection across y axis
b)
Reflection across x-axis
c)
180 Rotation
d)
Translation 2 units down
52.

Describe the transformation

f(x)+3f\left(x\right)+3  

a)

3 Units Up

b)

3 Units Down

c)

3 Units Left

d)

3 Units Right

53.

Describe the transformation

f(x−2)f\left(x-2\right)  

a)

2 Units Up

b)

2 Units Down

c)

2 Units Left

d)

2 Units Right

54.

Describe the transformation

f(x+5)f\left(x+5\right)  

a)

5 Units Up

b)

5 Units Down

c)

5 Units Left

d)

5 Units Right

55.

Describe the transformation

f(x)−6f\left(x\right)-6  

a)

6 Units Up

b)

6 Units Down

c)

6 Units Left

d)

6 Units Right

56.

Describe the transformation

f(x)−6f\left(x\right)-6  

a)

6 Units Up

b)

6 Units Down

c)

6 Units Left

d)

6 Units Right

57.

Describe the transformations

g(x+4)−6g\left(x+4\right)-6  

a)

4 Units Left

6 Units Up

b)

4 Units Left

6 Units Down

c)

4 Units Right

6 Units Up

d)

4 Units Right

6 Units Down

58.

Describe the transformations

−g(x)+2-g\left(x\right)+2  

a)

Reflected across the x-axis

2 Units Up

b)

Reflected across the x-axis

2 Units Down

c)

Reflected across the y-axis

2 Units Up

d)

Reflected across the y-axis

2 Units Down

59.

Describe the transformation

3h(x)3h\left(x\right)  

a)

Vertically Stretched by a factor of 3

b)

Vertically Compressed by a factor of 3

c)

Horizontally Stretched by a factor of 3

d)

Horizontally Stretched by a factor of 3

60.

Describe the transformation

h(13x)h\left(\frac{1}{3}x\right)  

a)

Vertically Stretched by a factor of 13\frac{1}{3}  

b)

Vertically Compressed by a factor of 13\frac{1}{3}  

c)

Horizontally Stretched by a factor of 13\frac{1}{3}  

d)

Horizontally Stretched by a factor of 13\frac{1}{3}  

61.

Describe the transformations

g(−x)−4g\left(-x\right)-4  

a)

Reflected across the x-axis

4 Units Left

b)

Reflected across the x-axis

4 Units Down

c)

Reflected across the y-axis

4 Units Left

d)

Reflected across the y-axis

4 Units Down

62.
How would you describe the translation from f(x)=x2  to  f(x)=(x-3)2 ?
a)
Horizontal translation: three units to the left
b)
Horizontal translation: three units to the right
c)
Vertical translation: three units up
d)
Vertical translation: three units down
63.

Describe the transformation of y = f(x) for the new function

y = - f(x)

a)

The graph of y = f(x) was flipped vertically across the x axis.

b)

The graph of y = f(x) was flipped horizontally across the y axis.

c)

The graph of y = f(x) was shifted down.

d)

The graph of y = f(x) was shifted right

64.

The graph of y=2x+3y=2^x+3  looks like the graph of the parent function  y=2xy=2^x  shifted ...

a)

up 3 units

b)

down 3 units

c)

3 units in the negative x direction (left)

d)

3 units in the positive x direction (right)

65.
f(x+2)
a)
Two up
b)
Two down
c)
Two left
d)
Two right
66.
f(x)+2
a)
Two up
b)
Two down
c)
Two left
d)
Two right
67.
If the blue is f(x)=x2, the red must be
a)
g(x)=(x+3)2
b)
g(x)=(x-3)2
c)
g(x)=x2+3
d)
g(x)=x2-2
68.
If the blue 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
69.
Name the parent function.
a)
quadratic
b)
cubic
c)
square root
d)
logarithmic
70.

Bob has $150 in his savings account and saves $40 per month. Which equation represents the amount Bob has in his account after x months?

a)

y = 150 + 40

b)

y = 40x + 150

c)

y = 150x + 40

d)

y = 40 + 150x

71.

The graph shows the cost, in dollars, for printing T-shirts at the T-shirt Shoppe.

Which linear equation can be used to represent the cost, y, for printing x T-shirts?

a)

y=5x+50y=5x+50  

b)

y=x + 50y=x\ +\ 50  

c)

y=10x+50y=10x+50  

d)

y=50x+5y=50x+5  

72.
Find the slope:
a)
3/4
b)
4/3
c)
-3/4
d)
-4/3
73.
Shift f(x)=x2 three units to the left and 4 units down
a)
f(x)=(x+3)2-4
b)
f(x)=(x-3)2-4
c)
f(x)=(x+4)2-3
d)
f(x)=(x-4)2-3
74.
How would you describe the translation from f(x)=x2  to  f(x)=(x-3)2 ?
a)
Horizontal translation: three units to the left
b)
Horizontal translation: three units to the right
c)
Vertical translation: three units up
d)
Vertical translation: three units down
75.

How has the parent graph y= x2x^2  been transformed?

a)

y=(x-4)2+1

b)

y=(x-4)2-1

c)

y=(x+4)2+1

d)

y=(x+4)2-1

76.
How would you describe the translation from f(x)=x2+2  to  f(x)=x2+7 ?
a)
Vertical translation: up 2 units
b)
Vertical translation: up 5 units
c)
Vertical translation: up 7 units
d)
Vertical translation: up 9 units
77.
How would you describe the translation from    f(x)=(x-2)2 to  f(x)=(x+3)2 ?
a)
Horizontal translation: to the right 3 units
b)
Horizontal translation: to the left 2 units
c)
Horizontal translation: to the left 5 units
d)
Horizontal translation: to the right 5 units
78.
Describe the translation from f(x)=(x+2)2-3  to  f(x)=(x-3)2-5
a)
Five units to the right, 2 units up
b)
Five units to the right, 2 units down
c)
Five units to the left, 2 units up
d)
Five units to the left, 2 units down
79.

Which equation shows a function that has been translated left 4 and 7 up?

a)

y = |x + 4| + 7

b)

y = (x - 4)2 + 7

c)

y = (x + 7)2 - 4

d)

y = |x + 4| - 7

80.
The graph shows the function f(x)=x2 in blue and another function g(x) in red.  Which could be the equation for g(x)?
a)
A.  g(x) = 2x2
b)
B.  g(x) = 1/2x2
c)
C.  g(x) = x2 + 2
d)
D.  g(x) = (x + 2)2
81.

Describe the transformations that map y=x2y=x^2  to:

a)

Translation left 1 unit, Vertical Stretch, Translation down 1 unit

b)

Vertical Compression, Translation right 1, Translation down 1

c)

Vertical stretch, Translate right 1 unit, Translation down 1 unit

d)

Translation left 1 unit, Horizontal stretch, Translation down 1 unit

82.
a)

moves right 3, Vertical Stretch , and down 4

b)

Horizontal stretch, moves right 3, and down 4

c)

moves right 3, Horizontal compression, and down 4

d)

Vertical stretch, moves left 3, and down 4

83.

What transformations happen to the function f(x) = -3(x - 4)2 ?

a)

left 3, down 4

b)

reflect down , vertical stretch 3, left 4

c)

reflect down, vertical stretch 3, right 4

d)

down 3, right 4

84.

Describe the transformation of y = f(x) for the new function

y = - f(x)

a)

The graph of y = f(x) was flipped vertically across the x axis.

b)

The graph of y = f(x) was flipped horizontally across the y axis.

c)

The graph of y = f(x) was shifted down.

d)

The graph of y = f(x) was shifted right

85.

Choose the correctly transformed function from y=x2y=x^2  

a)

f(x)= -(x+1)2+4

b)

f(x)= (x-1)2-4

c)

f(x)= -(x+1)2-4

d)

f(x)= -(x+4)2-1

86.
(x, y) -------> (x, -y) is a reflection over the x axis.       
a)
True
b)
False
87.
(x, y) -------> (x - 3, y) is a translation of 3 units to the left.   
a)
True
b)
False
88.
(x, y) -------> (x, y - 2) is a translation of 2 units up.  
a)
True
b)
False
89.
How does reflecting a figure over the y-axis change the ordered pair?
a)
Changes the x-coordinate
b)
Changes the y-coordinate
90.

Does the equation vertically stretch, compress, or reflect?

f(x)=0.75x2f\left(x\right)=0.75x^2  
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 2

b)

Compress by a factor of 0.75

c)

Reflect across the x-axis

d)

Both stretch by a factor of 2 and reflect across the x-axis

91.

Does the equation vertically stretch, compress, or reflect?

f(x)= 2x2f\left(x\right)=\ 2x^2  
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 2

b)

Compress by a factor of 2

c)

Reflect across the y-axis

d)

Both Stretch by a factor of  12\frac{1}{2}  & Reflect across the x-axis

92.

Does the equation vertically stretch, compress, or reflect?
f(x)=−x2f\left(x\right)=-x^2  
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 2

b)

Compress by a factor of  −2-2  

c)

Reflect across the x-axis

d)

Both Compress by 2 and Reflect across the x-axis

93.

Does the equation vertically stretch, compress, or reflect?
f(x)=−5x2f\left(x\right)=-5x^2  
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 5

b)

Compress by a factor of  52\frac{5}{2}  

c)

Reflect across the x-axis

d)

Both Stretch by a factor of 5 & Reflect across the x-axis

94.

Does the equation vertically stretch, compress, or reflect?
f(x)=14x2f\left(x\right)=\frac{1}{4}x^2  
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of  14\frac{1}{4}  

b)

Compress by a factor of  14\frac{1}{4}  

c)

Reflect across the x-axis

d)

Both Compress by a factor of 2 & Reflect across the x-axis

95.

Does the equation vertically stretch, compress, or reflect?
f(x)=0.5x2f\left(x\right)=0.5x^2  
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 0.5

b)

Compress by a factor of 0.5

c)

Reflect across the x-axis

d)

Both Compress by a factor of 0.5 & Reflect across the x-axis

96.

Does the equation vertically stretch, compress, or reflect?
f(x)=10x2f\left(x\right)=10x^2  
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 10

b)

Compress by a factor of 2

c)

Reflect across the x-axis

d)

Both Compress by a factor of 10 & Reflect across the x-axis

97.

Does the equation vertically stretch, compress, or reflect?
f(x)=−7x2f\left(x\right)=-7x^2  
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 7

b)

Compress by a factor of  −7-7  

c)

Reflect across the x-axis

d)

Both Stretch by a factor of 7 & Reflect across the x-axis

98.

Does the equation vertically stretch, compress, or reflect?
f(x)=17x2f\left(x\right)=\frac{1}{7}x^2  
*Always compare to the parent function (graph first)*

a)

Stretch

b)

Compress

c)

Reflect

d)

Both Compress & Reflect

99.

What is the parent function of a quadratic?

a)

y=x2y=x^2

b)

y=xy=x

c)

y=xy=\sqrt{x}

d)

y=∣x∣y=\left|x\right|

100.

Identify the steps for identifying the translations of quadratic functions.

a)

Graph the parent function

b)

Solve for y

c)

Solve for x

d)

Graph the given equation

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