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Function Transformations - Quadratics & Absolute Value

Total questions: 30

Worksheet time: 15hrs 0mins

Name
Class
Date
1.
Which transformation transforms the graph of
f(x) = x2 to the graph of
g(x) = (x + 4)2?
a)
a vertical translation 4 units up
b)
a vertical translation 4 units down
c)
a horizontal translation 4 units to the left
d)
a horizontal translation 4 units to the right
2.
How did we transform from f(x) =x2 
to
g(x) = -3x2
a)
reflection in x-axis and vertical shift down
b)
reflection x-axis and vertical stretch
c)
horizontal stretch
d)
reflection x-axis and vertical compression
3.
How did we transform from the parent function?
g(x) = -1/5(x - 1)2 + 7
a)
reflection, vertical compression, horizontal right, vertical up
b)
vertical compression, horizontal shift left, vertical shift up
c)
reflection, horizontal shift right, vertical shift down
d)
no changes were made to y = x2
4.
In the equation f(x)=5(x+3)2-10 what does the 5 do?
a)
Vertical stretch by 5
b)
Horizontal compress by 5
c)
Reflect
d)
Move up 5
5.
What is the vertical shift of this equation?
f(x) = -(x + 3)2 - 5
a)
left 5
b)
right 5
c)
up 5
d)
down 5
6.
What transformations occurred to get f(x), the red graph, to become g(x), the blue graph?
a)
horizontal shift down and vertical shift left
b)
horizontal shift left and vertical shift down
c)
horizontal shift right and vertical shift up
d)
horizontal shift up and vertical shift right
7.
What transformations have occurred? 
a)
Right 2 and up 2
b)
Left 2 and up 2
c)
Right 2 and down 2
d)
Left 2 and down 2
8.
What are the transformations?
y = (x - 2)2 + 4
a)
shift 2 units right
shift 4 units up
b)
shift 2 units left
shift 4 units up
c)
shift 2 units right
shift 4 units down
d)
shift 2 units left
shift 4 units up
9.
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
10.
What is the horizontal shift of this equation?
y = -(x + 3)2 - 5
a)
left 3
b)
right 3
c)
left 5
d)
right 5
11.
The quadratic parent function is
a)
y = x
b)
f(x) = x
c)
f(x) = x2
d)
y = √x
12.
y = (x + 2)2 + 9
This graph shifts... 
a)
Left 2, down 9
b)
Left 2, up 9 
c)
Right 2, up 9
d)
Right 2, down 9 
13.

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

14.

Describe the transformation:

f(x)=(x+3)2−2f\left(x\right)=\left(x+3\right)^2-2  

a)

right 3, down 2

b)

up 3, left 2

c)

left 3, up 2

d)

left 3, down 2

15.

Match the equation to its description.

a)

Vertically stretched by 2 and shifted up 4

b)

Vertically compressed by 2 and shifted up 4

c)

Vertically stretched by 2 and shifted left 4

d)

Vertically compressed by 2 and shifted left 4

16.

Identify all of the trasformations for the following function:

y=∣x−1∣+3y=\left|x-1\right|+3

a)

Left 1

b)

Right 1

c)

Up 1

d)

Up 3

e)

Reflect over x-axis

17.

Identify all of the transformations for the following function:

y=−2∣x+3∣y=-2\left|x+3\right|

a)

Vertical Stretch

b)

Right 3

c)

Vertical Compression

d)

Reflection over the x-axis

e)

Left 3

18.

Identify all of the transformations for the following function:

y=23∣x∣+5y=\frac{2}{3}\left|x\right|+5

a)

Right 5

b)

Up 5

c)

Down 5

d)

Vertical Compression

e)

Vertical Stretch

19.

Identify all of the transformations for the function shown.

a)

Reflection over the x-axis

b)

Right 3

c)

Left 3

d)

Up 2

e)

Down 2

20.

Identify the graph of the equation to the left.

a)

b)

c)

d)

21.

Describe the transformation of the equation below:

y = I x - 2 I + 4

a)

Left 2 up 4

b)

Right 2 up 4

c)

Left 2 down 4

d)

Right 2 down 4

22.

Describe the transformation of the equation below:

y = I x + 2 I - 5

a)

Left 2 up 5

b)

Right 2 up 5

c)

Left 2 down 5

d)

Right 2 down 5

23.

What are the transformations for the equation below:

y=-3|x+1|-3 ?

a)

Reflection, stretch factor of 3, left 1, and down 3

b)

Reflection, shrink factor of 3, right 1, and down 3

c)

Down 6 and right 1

d)

More narrow, right 1, and down 3

24.
Write an absolute value function given the following transformations:
Vertical Stretch of 2
Horizontal shift left 1 unit
Vertical shift down 9 units
a)
f(x) = |2x + 1| - 9
b)
f(x) = |2x - 1| - 9
c)
f(x) = 2|x + 1| - 9 
d)
f(x) = 2|x - 1| - 9
25.
Write an absolute value function given the following transformations:
Reflection across the x-axis
Vertical shift right 2 units
Horizontal shift down 7 units
a)
y = -|x + 2| - 7 
b)
y = |x - 2| - 7 
c)
y = -|x - 2| - 7
d)
y = -|x - 2| + 7
26.
What is the parent function for an absolute value function?
a)
f(x)=x3
b)
f(x)=x
c)
f(x)=IxI
d)
f(x)=x2
27.

Describe the transformation of the equation below from the parent function of y = I x I

y = -2 I x - 3 I + 3

a)

reflected over x axis, vertical stretched by 2, right 3, up 3

b)

reflected over x axis, vertical stretched by 2, left 3 up 3.

c)

reflected over x axis, vertical compression by 2, right 3, up 3

d)

reflected over the x axis, vertical compression by 2, left 3, up 3

28.

Describe the transformations from the parent graph to f(x) = -3∣x + 5∣ - 7

a)

reflection over x-axis, vertical stretch by 3, left 5, down 7

b)

reflection over y-axis, vertical stretch by 3, right 5, up 7

c)

reflection over x-axis, vertical compression by 3, left 5, down 7

d)

reflection over y-axis, vertical compression by 3, right 5, up 7

29.
What is the parent function for absolute values?
a)
y = x
b)
y = |x|
c)
y = x2
d)
y = 2x
30.

Which of the following describes the horizontal and vertical translations of the following function:

f(x)=∣x+4∣−9f(x)=|x+4|-9  

a)

Left 4, up 9

b)

Left 4, down 9

c)

Right 4, up 9

d)

Right 4, down 9

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