Free Printable transformations Saturday

1.

Which equation describes the transformation of shifting f(x)=x² two units right?

a)

x² + 2

b)

x² - 2

c)

(x + 2)²

d)

(x - 2)²

2.

Match the description to its equation.
Moves right 7

a)

A

b)

B

c)

C

d)

D

3.

Match the description to its equation.
-Moves left 2

a)

A

b)

B

c)

C

d)

D

4.

.
The blue is f(x)=|x|, red must be

a)

g(x)=|x+2|

b)

g(x)=|x|+2

c)

g(x)=|x-2|

d)

g(x)=|x|-2

5.

.
If the blue is f(x)=x^2,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

6.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

7.

Which equation describes the transformation of shifting f(x)=x³ four units down?

a)

x³+ 4

b)

x³- 4

c)

(x - 4)³

d)

(x + 4)³

8.

Describe the transformation

$f\left(x\right)+3$

a)

3 Units Up

b)

3 Units Down

c)

3 Units Left

d)

3 Units Right

9.

Describe the transformation

$f\left(x-2\right)$

a)

2 Units Up

b)

2 Units Down

c)

2 Units Left

d)

2 Units Right

10.

Describe the transformation

$f\left(x+5\right)$

a)

5 Units Up

b)

5 Units Down

c)

5 Units Left

d)

5 Units Right

11.

Describe the transformation

$f\left(x\right)-6$

a)

6 Units Up

b)

6 Units Down

c)

6 Units Left

d)

6 Units Right

12.

Describe the transformations

$g\left(x+4\right)-6$

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

13.

Describe the transformations

$-g\left(x\right)+2$

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

14.

Describe the transformation

$3h\left(x\right)$

a)

Vertical Stretch by a factor of 3

b)

Vertical Shrink by a factor of 3

c)

Horizontal Stretch by a factor of 3

d)

Horizontal Shrink by a factor of 1/3

15.

Describe the transformation

$h\left(\frac{1}{3}x\right)$

a)

Vertical Stretch by a factor of $\frac{1}{3}$

b)

Vertical Shrink by a factor of $\frac{1}{3}$

c)

Horizontal Stretch by a factor of 3

d)

Horizontal Shrink by a factor of $\frac{1}{3}$

16.

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

a)

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

b)

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

c)

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

d)

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

17.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

18.

Tell how the function transformed from y =|x|
y = -2|x|

a)

Translated left 2 units

b)

Reflected over x-axis

c)

Vertical Stretch by a factor of 2 and reflected over x-axis

d)

Vertical Shrink by a Factor of 2 and reflected over the x-axis

19.

Describe the transformations from the original parent function f(x) = x².
g(x) = 5x² + 2

a)

Vertical Stretch of 5
Down 2

b)

Vertical Shrink of 5
Up 2

c)

Vertical Stretch of 5
Up 2

d)

Vertical Shrink of 5
Down 2

20.

Describe the parent graph transformation

a)

Vertical stretch by 1/2, left 1, down 3

b)

Vertical stretch by 1/2, right 1, down 3

c)

Vertical Shrink by 1/2, left 1, down 3

d)

Vertical Shrink by 1/2, right 1, down 3

21.

The original graph is f(x). The new graph has been moved right 4 and up 3. The new graph is:

a)

$f(x+3)-4$

b)

$f(x-4)+3$

c)

$f(x+4)+3$

d)

$f(x+3)+4$

22.

f(x) has been moved two to the left

a)

$f(x+2)$

b)

$f(x)+2$

c)

$f(x-2)$

d)

$f(x)-2$

23.

Which function has a shift right 3?

a)

$f(x-3)$

b)

$f(x+3)$

c)

$f(x)+3$

d)

$f(x)-3$

24.

Challenge: Which transformation is NOT part of the function notation below?

-2f\left(x-3\right)

a)

Reflect across the x-axis

b)

shift 3 units down

c)

stretch factor of 2

d)

shift 3 units right

25.

What does the transformation $f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$ do to the graph of $f\left(x\right)$ ?

a)

shifts it left 1 unit and down 9 units

b)

shifts it right 1 unit and down 9 units

c)

shifts it right 9 units and up 1 unit and

d)

shifts it left 9 units and down 1 unit

26.

What does the transformation $f\left(x\right)\ \rightarrow\ \frac{1}{3}f\left(x\right)+4$ do to the graph of $f\left(x\right)$ ?

a)

Shrinks the graph vertically by a factor of $\frac{1}{3}$ and shifts up 4 units.

b)

Stretches the graph by a factor of $\frac{1}{3}$ and shifts up 4 units.

c)

Shifts the graph left $\frac{1}{3}$ of a unit and up 4 units.

d)

Shifts the graph right 3 units and down 4 units.

27.

Describe the transformation that occurred: $p(x)=f(x+3)$

a)

shift right 3

b)

stretch factor of 3

c)

shift up 3

d)

shift left 3

28.

$h(x)=f(x)+2$

Describe the transformation that occurred.

a)

Shift up 2 units

b)

Shift left 2 units

c)

Stretch factor of 2

d)

Shift right 2 units

29.

$w(x)=f(x-7)$

Describe the transformation that occurred.

a)

Shift down 7

b)

Shift up 7

c)

Shift right 7

d)

Shrink factor of 7

30.

$m(x)=f(x+1)$

Describe the transformation that occurred.

a)

Shift left 1 unit

b)

Shift right 1 unit

c)

Vertical stretch factor of 1

d)

Shift up 1 unit

31.

What is the transformation from $g\left(x\right)$ to $g(x-3)+5$

a)

Shift right 3, up 5

b)

Shift left 3, up 5

c)

Shift left 3, down 5

d)

Shift right 3, down 5

32.

If the graph of $f\left(x\right)$ has a stretch factor of 3 and is shifted 7 units up, what is the new function $g\left(x\right)$ ?

a)

$g(x)=f(x+7)+3$

b)

$g(x)=3f(x)+7$

c)

$g(x)=f(x-3)+7$

d)

$g\left(x\right)=3\left(x+7\right)$

33.

Which has a shift 2 units to the right?

a)

$f(x)+2$

b)

$f(x)-2$

c)

$f(x+2)$

d)

$f(x-2)$

34.

$h(x)=\frac{1}{5}f(x)$

Describe the transformation that occurred

a)

stretch factor of $\frac{1}{5}$

b)

shrink factor of $\frac{1}{5}$

c)

shift up $\frac{1}{5}$

d)

shift left $\frac{1}{5}$

35.

$h\left(x\right)=\frac{2}{3}p\left(x\right)$

Identify the transformation

a)

stretch factor of $\frac{2}{3}$

b)

shrink factor of $\frac{2}{3}$

c)

reflection over the x-axis

d)

shift down $\frac{2}{3}$

36.

Which of the following have a reflection over the x-axis? Select all that apply.

a)

undefined

b)

$y=\sqrt{x-3}+2$

c)

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

d)

$y=4\left|x\right|+2$

37.

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

a)

-f(x)

b)

f(-x)

c)

f^-1(x)

d)

f(2x)

38.

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

a)

(-2, 5)

b)

(-6, 5)

c)

(-4, 3)

d)

(-4, 7)

39.

a)

$𝑦=𝑓(𝑥)+2$

b)

$𝑦=𝑓(𝑥)−2$

c)

$𝑦=𝑓(𝑥+2)$

d)

$𝑦=𝑓(𝑥−2)$

40.

a)

$𝑦=𝑓(𝑥)+2$

b)

$𝑦=𝑓(𝑥)−2$

c)

$𝑦=𝑓(𝑥+2)$

d)

$𝑦=𝑓(𝑥−2)$

41.

a)

$𝑦=𝑓(𝑥)+3$

b)

$𝑦=𝑓(𝑥)−3$

c)

$𝑦=𝑓(𝑥+3)$

d)

$𝑦=𝑓(𝑥−3)$

42.

a)

$𝑦=𝑓(𝑥)+3$

b)

$𝑦=𝑓(𝑥)−3$

c)

$𝑦=𝑓(𝑥+3)$

d)

$𝑦=𝑓(𝑥−3)$

43.

a)

$𝑦=𝑓(𝑥+5)+3$

b)

$𝑦=𝑓(𝑥−5)−3$

c)

$𝑦=𝑓(𝑥+5)−3$

d)

$𝑦=𝑓(𝑥−5)+3$

44.

a)

$𝑦=𝑓(𝑥)+2$

b)

$𝑦=𝑓(𝑥)−2$

c)

$𝑦=𝑓(𝑥+2)$

d)

$𝑦=𝑓(𝑥−2)$

45.

a)

$𝑦=𝑓(2𝑥)$

b)

$𝑦=𝑓(1/2𝑥)$

c)

$𝑦=2𝑓(𝑥)$

d)

$𝑦=1/2𝑓(𝑥)$

46.

a)

$𝑦=𝑓(2𝑥)$

b)

$𝑦=𝑓(1/2𝑥)$

c)

$𝑦=2𝑓(𝑥)$

d)

$𝑦=1/2𝑓(𝑥)$

47.

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

a)

Vertical Compression by a factor of 2

b)

Vertical Stretch by a factor of 2

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

48.

Describe the transformation that occurred

h(x) = 1/5f(x)

a)

vertical stretch by 5

b)

vertical compression by 5

c)

vertical translation by 5

d)

vertical translation by -5

49.

Which of the following transformations are present (select all that apply)?

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

a)

reflection over horizontal axis

b)

reflection over vertical axis

c)

horizontal compression

d)

vertical shift

e)

Rotation about origin

50.

Which of the following transformations are present?
-2f(x - 1) + 2

a)

Shift 1 unit down

b)

Shift 1 unit up

c)

Shift 1 unit left

d)

Shift 1 unit right

51.

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

a)

f(x + 3) - 4

b)

f(x - 4) + 3

c)

f(x + 4) + 3

d)

f(x + 3) + 4

52.

If the original graph is f(x), and the new graph has been moved two to the left, what would be the new graph in f(x) notation?

a)

f(x + 2)

b)

f(x) + 2

c)

f(x - 2)

d)

f(x) - 2

53.

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

a)

f(x - 3)

b)

f(x + 3)

c)

f(x) + 3

d)

f(x) - 3

54.

Describe the transformation of y = f(x) to the new function
y = f(1/5x)

a)

Horizontal shrink by a factor of 1/5

b)

Vertical stretch be a factor of 5

c)

Vertically shrink by a factor of 1/5

d)

Horizontal stretch by a factor of 5

55.

What is the transformation?

a)

Shift up 1

b)

Shift down 1

c)

Shift left 1

d)

Shift right 1

56.

What is the transformation?

a)

Shift up 2

b)

Shift down 2

c)

Shift left 2

d)

Shift right 2

57.

What is the transformation?

a)

shift up 2 and right 1

b)

shift down 2 and left 1

c)

shift left 2 and up 1

d)

shift right 2 and down 1

58.

What is the transformation?

a)

Shift left 2

b)

Shift down 2

c)

None

d)

Reflection across the x-axis

59.

How has the function $f\left(x\right)=7\left(3\right)^x-5$ been transformed from the parent function?

a)

Shift up 5

Vertical stretch (SF 3)

b)

Shift down 5

Vertical stretch (SF 7)

c)

Shift up 5

Vertical stretch (SF 7)

d)

Shift down 5

Vertical stretch (SF 3)

60.

How has the function $f\left(x\right)=-5\left(3\right)^x$ been transformed from the parent function?

a)

Shifted up 5,

Reflected over x-axis

b)

Shifted down 5,

Vertical stretch (SF 5)

c)

Reflected over x-axis,

Vertical stretch (SF 5)

d)

Shifted down 5,

Reflected over x-axis

61.

How has the function $f\left(x\right)=\frac{1}{3}\left(3\right)^x-4$ been transformed from the parent function?

(choose two answers)

a)

Shifted left 4

b)

Shifted down 4

c)

Horizontal stretch (SF 1/3)

d)

Reflection over the x-axis

e)

Vertical stretch (SF 3)

62.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

a)

4 units up

b)

4 units to the left

c)

4 units to the right

d)

4 units down

63.

What transformations have happened to f(x) = 2^x if the new equation is
g(x) = -2^(x+3) -6

a)

It stayed the same

b)

reflects, up 3, left 6

c)

reflects, right 3, down 6

d)

reflects, left 3, down 6

64.

Describe the transformation(s) of the function when compared to its parent function.

a)

Translation left 3 units

b)

Translation down 3 units

c)

Horizontal stretch by a factor of -1

d)

Reflected across x-axis

65.

Describe the transformation(s) of the function when compared to its parent function.

a)

Translation up 2 units and translation right 1 unit

b)

Translation down 2 units and Translation left 1 unit

c)

Translation left 2 units and Translation up 1 unit

d)

Translation right 2 units and Translation down 1 unit

66.

What transformations have happened to f(x) = 2^x if the new equation is

g(x) = -2^(x+3) -6

a)

reflects across the x-axis, translate right 3 units, translate up 6 units

b)

reflects across the x-axis, translate up 3 units, translate left 6 units

c)

reflects across the x-axis, translate right 3 units, translate down 6 units

d)

reflects across the x-axis, translate left 3 units, translate down 6 units

67.

Given g(x)=(1/2)^x

Write a function that is translated 5 units left and translated 4 units up.

a)

f(x)= (1/2)^x+5+ 4

b)

f(x)= (1/2)^x+4+ 5

c)

f(x)= (1/2)^x-5- 4

d)

f(x)= (1/2)^x+5- 4

68.

What equation would yield a transformation right 3 units if your initial function was y=2^x

a)

y=2^x-3

b)

y=2^x+3

c)

y=2^x+³

d)

y=2^x-³

69.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

a)

4 units up

b)

4 units to the left

c)

4 units to the right

d)

4 units down

70.

What kind of transformation is represented?

a)

up 1 unit

b)

left 1 unit

c)

right 1 unit

d)

down 1 unit

71.

What transformations occur in the following function?

a)

right 3, up 2

b)

left 3, up 2

c)

left 3, down 2

d)

right 3, down 2

72.

What transformations occur in the following function?

a)

right 3, up 2

b)

right 3, down 2

73.

Given g(x)=5^x

Write a function that is reflected over the y-axis and translated 4 units to the right.

a)

f(x)= -5^x-4

b)

f(x)= -5^x+4

c)

f(x)= 5^(x-4)

74.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

75.

Is this exponential growth or decay?

a)

Growth

b)

Decay

76.

What kind of shift happens with this function?

a)

shift 4 units up

b)

shift 4 units down

77.

What is the transformation?

a)

Horizontal Translation left 1

b)

Horizontal Translation right 1

78.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation left 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

79.

What equation would yield a transformation right 3 units if your initial function was y=2^x

a)

y=2^x-3

b)

y=2^x+3

c)

y=2^x+³

d)

y=2^x-³

80.

What kind of shift happens with this function?

a)

4 points up

b)

4 points to the left

c)

4 points to the right

d)

4 points down

81.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

82.

What kind of shift happens with this function?

a)

4 points up

b)

4 points to the left

c)

4 points to the right

d)

4 points down

83.

What is the transformation?

a)

Vertical Translation up 1

b)

Vertical Translation down 1

c)

Horizontal Translation left 1

d)

Horizontal Translation right 1

transformations Saturday

Total questions: 83

Worksheet time: 3hrs 26mins

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