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Linear Transformations

Total questions: 35

Worksheet time: 35mins

Name
Class
Date
1.
Describe the transformation of the equation below from the parent function of y = I x I
y = I x - 4 I 
a)

Left 4

b)

Right 4

c)

Up 4

d)

Down 4

2.
What are the transformations?
y=(x-2)3+4
a)
Horz shift right 2      Vert shift up 4
b)
Horz shift left 2    Vert shift up 4
c)
Horz shift right 2      Vert shift down 4
d)
Horz shift left 2      Vert shift up 4
3.
Which parent function matches the graph?
a)
y = |x|
b)
y = x
c)
y = x2
d)
y = 2x
4.
What type of function is shown?
a)
linear
b)
quadratic
c)
square root
d)
absolute value
5.
Name the parent function.
a)
linear
b)
quadratic
c)
cube root
d)
cubic
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.
What type of function is shown?
a)
cube root
b)
square root
c)
logarithm
d)
exponential
8.
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
9.

Which equation represents a translation 8 units down from the parent function  y=x2y=x^2  ?

a)

y=x2+8y=x^2+8

b)

y=x2−8y=x^2-8

c)

y=(x+8)2y=\left(x+8\right)^2

d)

y=(x−8)2y=\left(x-8\right)^2

10.

Given g(x) is obtained by transforming of h(x) and g(x)=h(x−1)+2g\left(x\right)=h\left(x-1\right)+2  , describe the transformations on  h(x).h\left(x\right).  

a)

translated 1 unit left and 2 units up

b)

translated 1 unit right and 2 units up

c)

translated 2 units left and 1 unit up

d)

translated 2 units right and 1 unit up

11.

Which of the following represents a translation 5 units up from the parent quadratic function?

a)

y = x2 - 5

b)

y = x2 + 5

c)

y = (x - 5)2

d)

y = (x + 5)2

12.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

13.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Strech

d)

right 2 units

14.

Describe the transformation that occurred.

w(x) = f(x - 7)

a)

Down 7

b)

Up 7

c)

Right 7

d)

vertical compression

15.

Describe the transformation that occurred

m(x) = f(x + 1)

a)

Left 1 Unit

b)

Right 1 unit

c)

vertical stretch

d)

up 1 unit

16.

Describe the transformation: f(x - 5)

a)

vertical shift up 5

b)

vertical shift down 5

c)

horizontal shift right 5

d)

horizontal shift left 5

17.

-f(x) + 2

a)

horizontal reflection, translation up 2

b)

vertical reflection, translation up 2

c)

vertical reflection, translation right 2

d)

vertical reflection, translation down 2

18.

Write in function form: translation 3 units right

a)

g(x) = f(x − 3)

b)

g(x) = f(x) − 3

c)

g(x) = -3f(x)

d)

g(x) = f(-3x)

19.

reflection over y-axis, shift right 1

a)

f(-x - 1)

b)

-f(x + 1)

c)

-f(x) - 1

d)

-f(x - 1)

20.

translation up 1

a)

f(x) + 1

b)

f(x - 1)

c)

f(x) - 1

d)

f(x + 1)

21.
Describe the transformation from dotted to solid.
a)
f(x + 4)
b)
f(x - 4)
c)
f(x) + 4
d)
f(x) - 4
22.
Describe the transformation from dotted to solid.
a)
-f(x)
b)
f(x - 4)
c)
f(x) - 4
d)
f(-x)
23.
Describe the transformation from dotted to solid.
a)
f(x + 5) + 3
b)
f(x +3) + 5
c)
f(x - 5) + 3
d)
f(x - 3) + 5
24.
What causes the graph of y = x2 to open downward?
a)
multiply the x2 by a fraction
b)
multiply the x2 by a decimal
c)
multiply the x2 by a negative number
d)
multiply the x2 by a number greater than 1
25.
What are the transformations?
y=(x-2)3+4
a)
Horz shift right 2      Vert shift up 4
b)
Horz shift left 2    Vert shift up 4
c)
Horz shift right 2      Vert shift down 4
d)
Horz shift left 2      Vert shift up 4
26.
What type of function is shown?
a)
absolute value
b)
quadratic
c)
linear
d)
exponential
27.

What is the linear parent function?

a)

y = x

b)

y = mx + b

c)

f(x) = 2x

d)

Not here

28.

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

a)

Graph g is a reflection.

b)

Graph g translated down 2 units.

c)

Graph g is steeper.

d)

Graph g is less steep.

29.

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

a)

Graph g rotated

b)

Graph g translated down 4 units

c)

Graph g translated up 4 units

d)

Graph g reflected

30.
a)
Left 2, Down 2, Vertical Stretch
b)
Right 2; Up 1; 
c)
Vertical Stretch; Right 2; Up 1
d)
Left 2; Down 2;
31.
a)
Left 2; Down 1
b)
Reflection over x-axis; Left 2; Up 1
c)
Reflection over x-axis; Left 2; Down 1
d)
Reflection over y-axis; Right 2; Down 1
32.
a)
Cube Root
b)
Square Root
c)
Quadratic Root
d)
Cubic
33.
a)
Square Root
b)
Quadratic
c)
Cube Root
d)
Cubic
34.
a)
f(x)=x2 + 2
b)
f(x) = (x-2)2 + 1
c)
f(x)= (x+2)2 - 1
d)
f(x)= (x+2)2 + 1
35.
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

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