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Practice on Transformation of functions

Total questions: 25

Worksheet time: 32mins

Name
Class
Date
1.
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
2.
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
3.
Which equation below is a quadratic function translated left 4 units?
a)
y = x2 + 4
b)
y = (x + 4)2
c)
y = (x - 4)2
d)
y = 4x2
4.
Which equation is a quadratic function reflected over the x-axis and shifted up 2.
a)
y = x2 + 2
b)
y = -x2 + 2
c)
y = x2 - 2
d)
y = -(x + 2)2
5.

Match the equation with the graph:

a)

y = (x - 2)2 + 4

b)

y = -(x - 4)2 + 2

c)

y = -(x - 2)2 + 4

d)

y = -(x + 2)2 + 4

6.

Describe the transformations from the original parent function f(x) = x2.

g(x) = 5x2 + 2

a)

Vertical Stretch of 5

Vertical Down 2

b)

Vertical Compression of 5

Vertical Up 2

c)

Vertical Stretch of 5

Vertical Up 2

d)

Vertical Compression of 5

Vertical Down 2

7.

What are the transformations of this functions compared to the parent function y = √(x)?

a)

Horizontal right 5, vertical down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch of 2, and horizontal right 5

c)

Reflected over the x-axis, vertical stretch of -2, and horizontal left 5

d)

Horizontal right 5, Vertical down 2

8.
a)
f(x) = −(x−2)3−1
b)
f(x) = −(x+2)3−1
c)
f(x) = −(x−2)3 + 1
d)
f(x) = −(x+2)3 + 1
9.
a)
f(x)=3∣x−2∣−2
b)
f(x)=1/3∣x+2∣−2
c)
f(x)=3∣x+2∣−2
d)
f(x) = 1/3∣x−2∣+2
10.
What is the equation of this graph?
a)
f(x) = (x + 2)2 - 3
b)
f(x) = (x - 2)2 - 3
c)
f(x) = |x + 2| - 3
d)
f(x) = |x - 2| - 3
11.
What is the equation of the graph?
a)
y = √(x - 3)
b)
y = √(x) + 3
c)
y = √(x - 5) + 4
d)
y = √(x + 5) + 4
12.
Which equation represents this graph.
a)
f(x)=∣3x∣
b)
f(x)=2∣x∣-3
c)
f(x)=∣x∣
d)
f(x)=3∣x∣-2
13.
Which equation represents this graph.
a)
f(x)=(x - 4)2 - 3
b)
f(x)=-(x - 4)2 + 3
c)
f(x)=(x - 4)2 + 3
d)
f(x)=-(x + 4)2 + 3
14.

Describe the transformation from the parent absolute value function:

y=∣x∣−5y=\left|x\right|-5  

a)

Shift up 5 units

b)

Shift down 5 units

c)

Shift right 5 units

d)

Shift left 5 units

15.

Describe the transformation from the parent quadratic function:

y=(x−2)2y=\left(x-2\right)^2  

a)

Shift up 2 units

b)

Shift down 2 units

c)

Shift right 2 units

d)

Shift left 2 units

16.

Describe the transformation from the parent square root function:

y=x+4y=\sqrt[]{x+4}  

a)

Shift up 4 units

b)

Shift down 4 units

c)

Shift right 4 units

d)

Shift left 4 units

17.

Describe the transformation from the parent cubic function:

y=−x3+3y=-x^3+3  

* Select TWO answers *

a)

Shift up 3 units

b)

Shift down 3 units

c)

Reflection over the y-axis

d)

Reflection over the x-axis

18.

Describe the transformation from the parent quadratic function:

y=14x2y=\frac{1}{4}x^2  

a)

Vertical stretch by a factor of ¼

b)

Vertical compression by a factor of ¼

19.

Describe the transformation from the parent absolute value function:

y=8∣x∣y=8\left|x\right|  

a)

Vertical stretch by a factor of 8 

b)

Vertical compression by a factor of 8 

20.

Describe the transformation from the parent square root function:

y=2 x−5y=2\ \sqrt[]{x-5}  

* Select TWO answers *

a)

Vertical stretch

b)

Vertical compression

c)

Translation 5 units right

d)

Translation 5 units left

21.

Describe the transformation from the parent absolute value function:

y=−∣x+4∣−3y=-\left|x+4\right|-3  

* Select THREE answers *

a)

Reflection over the x-axis

b)

Translation 4 units left

c)

Translation 4 units up

d)

Translation 3 units left

e)

Translation 3 units down

22.

Describe the transformation from the parent cubic function:

y=(x+6)3−4y=\left(x+6\right)^3-4  

* Select TWO answers *

a)

Translation 6 units right

b)

Translation 6 units left

c)

Translation 4 units up

d)

Translation 4 units down

23.
. 
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
24.
a)
g(x)=x3+1
b)
g(x)=x3-1
c)
g(x)=(x-1)3
d)
g(x)=(x+1)3
25.
What is the equation of this graph?
a)

f(x) = 2(x + 2)2 - 3

b)

f(x) = 2(x - 2)2 - 3

c)

f(x) =2|x + 2| - 3

d)

f(x) = 2|x - 2| - 3

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