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Worksheets

Transformations

Total questions: 50

Worksheet time: 2hrs 40mins

Name
Class
Date
1.

f(x) = 2x

a)

Vertical stretch

b)

Vertical compression

c)

Vertical translation up

d)

Reflection over the x-axis

e)

No Transformation

2.

f(x) = x2 - 6

a)

Vertical translation up

b)

Vertical translation down

c)

Horizontal translation left

d)

Horizontal translation right

e)

Reflection over the x-axis

3.

What will be the vertex of

f(x) = 4 (x-3)2 + 1 ?

a)

(3,1)

b)

(1,3)

c)

(-3,1)

d)

(3, -1)

e)

None of these.

4.

Let the graph of g be a translation 2 units down and 4 units left of the graph of f(x) = x2. Write a rule for g.

a)

g(x) = (x - 4)2 - 2

b)

g(x) = (x + 4)2 - 2

c)

g(x) = (x - 4)2 + 2

d)

g(x) = (x + 4)2 + 2

5.

Let the graph of g be a vertical stretch by a factor of 5 of the graph of f(x) = x2. Write a rule for g.

a)

g(x) = 5x2

b)

g(x) = -5x2

c)

g(x) = x2 + 5

d)

g(x) = (x + 5)2

6.

Let the graph of g be a translation 7 units right and a reflection in the x-axis of the graph of f(x) = x2. Write a rule for g.

a)

g(x) = -(x - 7)2

b)

g(x) = (x - 7)2

c)

g(x) = -(x + 7)2

d)

g(x) = (x + 7)2

7.

Let the graph of g be a translation 7 units right and 12 units up of the graph of f(x) = (x + 3)2 - 8. Write a rule for g.

a)

g(x) = (x - 4)2 + 4

b)

g(x) = (x + 10)2 + 4

c)

g(x) = (x - 4)2 - 20

d)

g(x) = (x + 10)2 - 20

8.

Let the graph of g be a reflection in the x-axis of the graph of f(x) = x2 - 7. Write a rule for g.

a)

g(x) = x2 + 7

b)

g(x) = -x2 + 7

c)

g(x) = -x2 - 7

d)

g(x) = -7x2

9.

Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the x-axis of the graph of f(x) = x2 + 2. Write a rule for g.

a)

g(x) = 3x2 + 6

b)

g(x) = -3x2 - 6

c)

g(x) = -3x2 - 2

d)

g(x) = 3x2 + 2

10.

For g(x) = (x - 10)2 - 4, describe the transformation from the parent function.

a)

Shift left 10 and down 4 units

b)

Shift right 10 and down 4 units

c)

Shift left 10 and up 4 units

d)

Shift right 10 and up 4 units

11.

For g(x) = 2(x + 3)2, describe the transformation from the parent function.

a)

Vertical stretch by factor of 2, slide left 3 units

b)

Vertical stretch by factor of 2, slide right 3 units

c)

Slide up 2 units and left 3 units

d)

Slide up 2 units and right 3 units

12.

For g(x) = -x2 +13, describe the transformation from the parent function.

a)

Reflection in x-axis, slide up 13 units

b)

Reflection in x-axis, slide down 13 units

c)

Slide up 13 units

d)

Slide down 13 units

13.

For g(x) = -3(x - 6)2 + 2, choose the transformation from the parent function that does NOT occur.

a)

Reflection in the x-axis

b)

Vertical stretch by factor of 3

c)

Slide 6 units left

d)

Slide 2 units up

14.

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation.

a)

g(x) is shifted up 6 units

b)

g(x) is shifted down 6 units

c)

g(x) is shifted left 6 units

d)

g(x) is shifted right 6 units

15.
Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
a)
The graph of g is a vertical translation 2 units up of the graph of f
b)
The graph of f is a horizontal translation two units left of g
c)
The graph of g is a vertical stretch by a factor of 2 of the graph of f
d)
The graph of g is a reflection of the graph of f
16.

Which transformation will occur if f(x) = x is replaced with  14f(x)\frac{1}{4}f\left(x\right)  ?

a)

Vertical stretch by a factor of 4

b)

Vertical compression by a factor of 1/4

c)

Vertical translation up by 1/4 units.

d)

Horizontal compression by a factor of 1/4

17.

What is the linear parent function?

a)

y = x

b)

y = mx + b

c)

f(x) = 2x

d)

Not here

18.
If the graph of the parent function f(x) = x is shifted 7 units
down, which of the following equations would the new graphed
line represent?
a)
f(x) = 7x
b)
f(x) = x - 7
c)
f(x) = x + 7
d)
f(x) = 7x - 7
19.

Which of the following g(x) equations is vertically stretched and shifted down from f(x) = x?

a)

g(x) = 2 f(x) + 6

b)

g(x) = 1/2 f(x) + 6

c)

g(x) = 2 f(x) - 6

d)

g(x) = 1/2 f(x) - 6

20.

The linear parent function, f(x) = x, is transformed to g(x) = f(x) + 3. Describe the transformation.

a)

g(x) is shifted up 3 units

b)

g(x) is shifted down 3 units

c)

g(x) is shifted left 3 units

d)

g(x) is shifted right 3 units

21.

Which transformation on

f(x) = x

is g(x) = -f(x)

a)

Reflection across the y-axis

b)

The slope will be less steep

c)

The graph will be wider

d)

Reflection across the x-axis.

22.

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

a)

Graph g shifted down 3 units

b)

Graph g shifted down 4 units

c)

Graph g shifted up 4 units

d)

Graph g reflected

23.

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

a)

Graph g shifted down 6 units

b)

Graph g is steeper by a factor of 7

c)

Graph g is less steep by a factor of 1/3

d)

Graph g shifted up 6 units

24.

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

a)

Graph g reflected

b)

Graph g shifted up 2 units

c)

Graph g reflected and shifted down 2 units.

d)

Graph g reflected and shifted up 2 units

25.
Which transformation maps the graph of
f(x) = x2 to the graph of g(x) = (x + 4)2?
a)
a reflection across the line x = -4
b)
a reflection across the line y = -4
c)
a translation shifting f(x) 4 units to the left
d)
a translation shifting f(x) 4 units to the right
26.
Match the description to its equation.
Moves up 2
Moves left 4
a)
A
b)
B
c)
C
d)
D
27.
Match the description to its equation.
Moves right 7
a)
A
b)
B
c)
C
d)
D
28.
Match the description to its equation.
Moves down 1
Moves right 1
a)
A
b)
B
c)
C
d)
D
29.
Which transformation will occur if f(x) = x2 is replaced with -f(x)?
a)
Nothing happens, it stays the same.
b)
Vertical stretch by a factor of 2.
c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
30.
Which transformation will occur if f(x) = x2 is replaced with f(x) + 2?
a)
Nothing happens, it stays the same.
b)
Vertical stretch by a factor of 2.
c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
31.

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
32.
a)
g(x)=2x2
b)
g(x)=0.5x2
c)
g(x)=x2+2
d)
g(x)=(x+2)2
33.
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
34.
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
35.
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)=3x2
b)
B.  g(x)=1/3x2
c)
C.  g(x) = x2 - 3
d)
D.  g(x) = (x-3)2
36.

If f(x) is the red graph and g(x) is the blue graph, what transformation changes f(x) to g(x)?

a)

translation

b)

rotation

c)

reflection

d)

vertical stretch

37.

Which function DOES NOT represent a horizontal shift of the function f(x)=x2

a)

g(x)= x2+3

b)

g(x)= (x+3)2

c)

g(x)= (x-3)2

d)

g(x) =(x-2)2

38.

Where is the vertex of  y=3(x26)2+14y=3\left(x-26\right)^2+14  ?

a)

(26, 14)

b)

(14, 26)

c)

(-26, 14)

d)

(3, 14)

e)

(3, 26)

39.

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

a)

translates it left one unit and down 9 units

b)

translates it right one unit and down 9 units

c)

translates it up one unit and right 9 units

d)

translates it down one unit and left 9 units

40.

The linear parent function, f(x) = x, is transformed to g(x) = f(x + 3). Describe the transformation.

a)

g(x) is shifted up 3 units

b)

g(x) is shifted down 3 units

c)

g(x) is shifted left 3 units

d)

g(x) is shifted right 3 units

41.

Identify the vertex of f(x) = -2(x+1)2 + 3

a)

(h,k)

b)

(3, 1)

c)

(-1,-3)

d)

(-1,3)

42.

What steps transform the graph y = x2 to y = 2(x+2)2 - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

43.

What steps transform the graph y = x2 to y = (x-4)2

a)

Shifted down 4 units

b)

Shifted left 4 units

c)

Shifted right 4 units

d)

Shifted up 4 units

44.

Given f(x) = ax² , if 0 < a < 1 , the graph will transform by

a)

becoming wider or vertically compressed

b)

becoming narrower or vertically stretched

45.

Given f(x) = ax² , if a > 1 , the graph will transform by

a)

becoming wider or vertically compressed

b)

becoming narrower or vertically stretched

46.

In the vertex form f(x) = a(x - h)² + k , what does the 'h' value do?

a)

Shifts the function left or right

b)

Reflection over the x-axis

c)

Vertical stretch or compression

d)

Shifts the function up or down

47.
How did we transform from the parent function?
y = x2 + 2
a)
horizontal shift up
b)
vertical shift up
c)
horizontal shift down
d)
vertical shift down
48.

How did we transform from y=x2?

y = -3x2

a)

vertical reflection and vertical shift down

b)

vertical reflection and vertical stretch

c)

horizontal stretch

d)

vertical reflection and vertical compression

49.

Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?

a)

Horizontal shift left 6, vertical shift up 2

b)

Horizontal shift left 6, vertical shift down 2

c)

Horizontal shift right 6, vertical shift down 2

d)

Horizontal shift right 6, vertical shift up 2

50.
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