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Parent Function & Transformation

Total questions: 43

Worksheet time: 6hrs 30mins

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 left 4 units?
a)
y = x2 + 4
b)
y = (x + 4)2
c)
y = (x - 4)2
d)
y = 4x2
3.
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
4.
Name the parent function. 
a)
constant
b)
square root
c)
linear
d)
absolute value
5.
What type of function is shown?
a)
linear
b)
quadratic
c)
square root
d)
absolute value
6.
Which equation is an absolute value graph shifted right 5 units?
a)
y = |x - 5|
b)
y = |x + 5|
c)
y = |x| + 5
d)
y = -5|x|
7.
What shifts have occurred?
a)
left 1, up 5
b)
left 1, down 5
c)
right 1, down 5
d)
right 1, up 5
8.
What is the equation of the graph below?
a)
f(x) = I x + 2 I 
b)
f(x) = I x + 2 I +2
c)
f(x) = I x - 2 I +2
d)
f(x) = I x - 2 I 
9.

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

10.
Which transformation will occur if f(x) = x is replaced with f(x) + 2?
a)
Translation left 2 units
b)
Translation right 2 units
c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
11.

How did the equation shift from the parent function? y = f(x - 4)

a)

Shift right by 4

b)

Shift left by 4

c)

Horizontal Stretch by 4

d)

Vertical Stretch by 4

e)

Shift down by 4

12.
Describe the transformation of y = (x - 4)2
a)
Shift UP
b)
Shift DOWN
c)
Shift LEFT
d)
Shift RIGHT
13.
Describe the transformation
a)
left 2 up 5
b)
right 2 up 5
c)
left 2 down 5
d)
right 2 down 5
14.
Describe the transformation that is applied to the parent function. 
f(x) =  3 Ix+8I
a)
Stretches by 3, Shifts left 8
b)
Stretches by 3, Shifts right 8
c)
Stretches by 3, Shifts up 8
d)
Stretches by 3, Shifts down 8
15.
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)
16.
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
17.
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
18.
Compare the function y = 5x2 to the parent function y = x2
a)
Wider
b)
Narrower
19.
What are the transformations?
y=3(x-4)2?
a)

horizontal shift right 4,

narrower by a factor of 3

b)

horizontal shift

left 4,

narrower by a factor of 3

c)

horizontal shift right 4,

wider by a factor of 1/3

d)

horizontal shift right 4,

vertical shift up 3

20.
Describe the transformation of y = f(x) for the new function
f(x) = ⅔(x - 7)2 
a)

Wider by ⅔

Right 7

b)

Narrower by ⅔ Left 7

c)

Narrower by ⅔ Right 7

d)

Wider by ⅔

Left 7

21.
Describe the parent graph transformation
a)

narrower, left 1, down 3

b)

narrower, right 1, down 3

c)

wider, left 1, down 3

d)

wider, right 1, down 3

22.

What transformation occurs in y = 7∣x∣?

a)

Compression

b)

Stretch

c)

Reflection and compression

d)

Reflection and stretch

23.

What transformation occurs in y = -2/3x2?

a)

Reflection and compression

b)

Reflection and stretch

c)

Compression

d)

Stretch

24.

What transformation occurs in y = 1/2x2?

a)

Stretch

b)

Reflection and stretch

c)

Compression

d)

Reflection and compression

25.

Which equation transforms f(x) = x to a horizontal stretch by a factor of 2, a reflection over the x axis, and a shift down 4?

a)

f(-2x - 4)

b)

f(-1/2x) - 4

c)

-f(2x) - 4

d)

-f(1/2x) - 4

26.
Which of the following is the correct equation for the given graph?
a)
f(x) = -(x + 2)2 - 4
b)
f(x) = -(x - 2)2 - 4
c)
f(x) = -3(x - 2)2 - 4
d)
f(x) = -3(x + 2)2 - 4
27.
What type of function is shown?
a)
cube root
b)
square root
c)
logarithm
d)
exponential
28.
a)
y = - √(x + 1)
b)
y = √(x + 1)
c)
y = - √(x) - 1
d)
y = - √(x) + 1
29.
What is the equation of the graph below?
a)
f(x ) = I x + 4 I + 2
b)
f(x ) = -I x - 4 I + 2
c)
f(x ) = I x - 4 I + 2
d)
f(x ) = -I x + 4 I + 2
30.

Write an absolute value function given the following transformations:
Reflection across the x-axis
horizontal shift right 2 units
vertical shift down 7 units

a)
y = -|x + 2| - 7 
b)
y = |x - 2| - 7 
c)
y = -|x - 2| - 7
d)
y = -|x - 2| + 7
31.
What shifts have occurred?
a)
left 1, up 5
b)
left 1, down 5
c)
right 1, down 5
d)
right 1, up 5
32.
Name the parent function.
a)
linear
b)
quadratic
c)
cube root
d)
cubic
33.
The graph shows the function f(x)=x3 in blue and another function g(x) in red.  Which could be the equation for g(x)?
a)
A.  g(x) = -x3
b)
B.  g(x) = x3 - 1
c)
C.  g(x) = (x + 1)3
d)
D.  g(x) = (x - 1)3
34.
What transformations has the function undergone?
a)
reflect over y, vertical compress by 2, right 5, up 1
b)
reflect over x, horizontal compression by 2, left 5, up 1
c)
reflect over x, vertical stretch by 2, right 5, up 1
d)
reflect over y, horizontal stretch by -2, right 5, up 1
35.
Describe the transformation of the graph  
y = -(x - 4)3 + 5
a)
Up 5 and Left 4 
b)
Reflect x-axis, Left 4, Up 5
c)
Reflect x-axis, Right 4, Up 5
d)
Right 4 and up 5
36.
Identify the transformations to the step function: 
a)
x-axis reflection; stretch of 2; right 2; down 2
b)
x-axis reflection; stretch of 2; left 2; down 2
c)
x-axis reflection; shrink of 2; left 2; up 2
d)
shrink of -2; right 2; down 2
37.
Which of the following is the correct equation for the given graph?
a)
f(x) = (x - 2)2 - 1
b)
f(x) = (x + 2)2 - 1
c)
f(x) = -(x + 2)2 - 1
d)
f(x) = -(x - 2)2 - 1
38.

Which of the following is the graph of y = (x – 1)3 – 7?

a)
b)
c)
d)
39.
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
40.
The graph of
f(6x) 
represents what kind of transformation?
a)
Vertical stretch
b)
Vertical shrink
c)
Horizontal stretch
d)
Horizontal shrink
41.

 y=x−32+2y=\sqrt{x-\frac{3}{2}}+2  belongs to what family of functions?

a)

square root

b)

absolute value

c)

linear

d)

quadratic

42.
What is the equation of the PARENT  function?
a)
f(x) = 2x
b)
f(x) = x3
c)
f(x) = |x|
d)
f(x) = x
43.
Is this graph a function or not a function? 
a)
Function 
b)
Not a Function 

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