Quiz about Transformations of Parent Functions

Question 1

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

Accepted Answer

f(x - 3)

Answer

f(x + 3)

Answer

f(x) + 3

Answer

f(x) - 3

Question 2

If the original graph is f(x), and the new graph has been moved two to the left, what would be the new graph in f(x) notation?

Accepted Answer

f(x + 2)

Answer

f(x) + 2

Answer

f(x - 2)

Answer

f(x) - 2

Question 3

The original graph is f(x). The new graph has been reflected across the x axis. The equation for the new graph in f(x) notation is:

Accepted Answer

-f(x)

Answer

f(-x)

Question 4

The original graph is f(x). The new graph is vertically stretched by a factor of 2. What is the equation for the new graph?

Accepted Answer

2f(x)

Answer

f(2x)

Question 5

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

Accepted Answer

f(x - 4) + 3

Answer

f(x + 3) - 4

Answer

f(x + 4) + 3

Answer

f(x + 3) + 4

Question 6

The original graph is f(x). The new graph is up 5, left 3, and reflected across the x-axis.

Accepted Answer

-f(x + 3) + 5

Answer

f(x + 3) + 5

Answer

-f(x - 3) + 5

Answer

-f(x + 5) + 3

Question 7

The original graph is f(x). The new graph has been vertically stretched by a factor of 4 and translated down 4.

Accepted Answer

4f(x) - 4

Answer

f(4x - 4)

Answer

4f(x -4)

Answer

f(4x) - 4

Question 8

The original graph is f(x). The new graph is translated 5 down, reflected across the x-axis, and translated 3 to the left.

Accepted Answer

-f(x + 3) - 5

Answer

f(x + 3) - 5

Answer

-f(x - 5) + 3

Answer

f(-x + 3) -5

Question 9

Which vocabulary word refers to changing the position on the x-axis or y-axis? (i.e. moving up, down, left, and right)

Accepted Answer

Translations

Answer

Dilations

Answer

Reflections

Answer

Transformations

Question 10

Identify the transformation from the graph of f(x)=x²to the graph g(x)= x² - 5

Accepted Answer

shifted down five units

Answer

shifted up five units

Answer

shifted left five units

Answer

shifted right five units

Question 11

Identify the transformation from the graph of f(x)=x²to the graph g(x)= (x+5)²

Accepted Answer

shifted left 5 units

Answer

shifted up five units

Answer

shifted down five units

Answer

shifted right 5 units

Question 12

Identify the transformation from the graph of f(x)=x²to the graph g(x)= x² + 5

Accepted Answer

shifted up five units

Answer

shifted down five units

Answer

shifted left five units

Answer

shifted right five units

Question 13

Identify the transformation from the graph of f(x)=x²to the graph g(x)= (x - 5)²

Accepted Answer

shifted right five units

Answer

shifted up five units

Answer

shifted down five units

Answer

shifted left five units

Question 14

Write an equation for the graph below.

Accepted Answer

f(x) = (x-2)² + 1

Answer

f(x)=x² + 2

Answer

f(x)= (x+2)² - 1

Answer

f(x)= (x+2)² + 1

Question 15

The blue is f(x)=|x|, red must be ____?

Accepted Answer

g(x) =|x-2|

Answer

g(x) =|x+2|

Answer

g(x) =|x|+2

Answer

g(x) =|x|-2

Question 16

. If the blue is f(x)=x^2,then the red must be ___?

Accepted Answer

g(x)=x2-5

Answer

g(x)=x2+5

Answer

g(x)=(x-5)²

Answer

g(x)=(x+5)²

Question 17

Which equation describes the transformation of shifting f(x)=x³ three units left?

Accepted Answer

(x + 3)3

Answer

x3 + 3

Answer

x3 - 3

Answer

(x - 3)3

Question 18

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

Accepted Answer

Right 3 and up 5

Answer

Left 3 and up 5

Answer

Right 3 and down 5

Answer

Left 3 and down 5

Question 19

Identify the transformation from the graph of f(x)=x²to the graph g(x)= -(x+5)²

Accepted Answer

shifted left 5 units
reflection x-axis

Answer

shifted up five units
reflection in x-axis

Answer

shifted down five units
reflection in x-axis

Answer

shifted right 5 units
reflection x-axis

Question 20

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

Accepted Answer

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

Answer

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

Answer

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

Answer

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

Question 21

Question 21.

Accepted Answer

Vertical Stretch 2, Translate Left 3 and Down 4

Answer

Vertical Stretch 2, Translate Right 3 and Down 4

Answer

Vertical Stretch 2, Translate Right 3 and Up 4

Answer

Vertical Stretch 2, Translate Left 3 and Up 4

Question 22

Question 22.

Accepted Answer

Translate Down 1

Answer

Translate left 1

Answer

Translate Right 1

Answer

Translate Up 1

Question 23

Question 23.

Accepted Answer

Vertical Stretch 2, translate right 1

Answer

Vertical compression 2, translate right 1

Answer

Vertical Stretch 2, translate left 1

Answer

Vertical compression 2, translate left 1

Question 24

Question 24.

Accepted Answer

Translate right 2

Answer

Translate left 2

Answer

Translate up 2

Answer

Translate down 2

Question 25

Question 25.

Accepted Answer

Translate up 3

Answer

Translate down 3

Answer

Translate right 3

Answer

Translate left 3

Question 26

Question 26.

Accepted Answer

Translate left 5 and down 2

Answer

Translate left 2 and up 5

Answer

Translate right 2 and down 5

Answer

Translate right 5 and up 2

Question 27

Question 27.

Accepted Answer

Reflect over the x-axis, Vertical stretch by 3, translate left 1

Answer

Reflect over the x-axis, Vertical compression by 3, translate right 1

Answer

Reflect over the x-axis, Vertical compression by 3, translate left 1

Answer

Reflect over the x-axis, Vertical stretch by 3, translate right 1

Question 28

Question 28.

Accepted Answer

Vertical compression by 3/4, translate up 5

Answer

Vertical compression by 3/4, translate down 5

Answer

Vertical compression by 3/4, translate left 5

Answer

Vertical compression by 3/4, translate right 5

Question 29

Question 29.

Accepted Answer

Reflect over the x-axis, vertical compression by 0.2, translate up 1

Answer

Reflect over the x-axis, vertical stretch by 0.2, translate up 1

Answer

Reflect over the y-axis, vertical stretch by 0.2, translate up 1

Answer

Reflect over the y-axis, vertical compression by 0.2, translate up 1

Question 30

Question 30.

Accepted Answer

Vertical stretch by 6, translate left 9 and up 1

Answer

Vertical stretch by 6, translate left 9 and down 1

Answer

Vertical stretch by 6, translate right 9 and up 1

Answer

Vertical stretch by 6, translate right 9 and down 1

Question 31

What does h do to a parent function?

Accepted Answer

Translate left/right

Answer

Vertical compression/stretch

Answer

Reflection

Answer

Translate up/down

Question 32

What does k do to a parent function?

Accepted Answer

Translate up/down

Answer

Vertical stretch/compression

Answer

Reflect over the x-axis

Answer

Translate left/right

Question 33

Select all of the following transformations that a can cause.

Accepted Answer

Reflection

Accepted Answer

Vertical stretch

Accepted Answer

Vertical compression

Answer

Translate

Question 34

Which of the following is the general form for a transformed parent function?

Accepted Answer

g(x)=af(x-h)+k

Answer

g(x)=af(x+h)+k

Answer

g(x)=af(x-h)-k

Answer

g(x)=af(x-k)+h

Question 35

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

Accepted Answer

a translation shifting f(x) 4 units to the left

Answer

a translation shifting f(x) 4 units up

Answer

a translation shifting f(x) 4 units down

Answer

a translation shifting f(x) 4 units to the right

Question 36

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

Accepted Answer

Vertical translation up by 2 units.

Answer

Translation left 2 units

Answer

Narrower

Answer

Reflection across the x-axis.

Question 37

Describe the transformation of y = f(x) for the new function
y = f(x) + 5

Accepted Answer

The graph of y = f(x) was shifted up 5 units.

Answer

The graph of y = f(x) was shifted to the right 5 units.

Answer

The graph of y = f(x) was shifted to the left 5 units.

Answer

The graph of y = f(x) was shifted down 5 units.

Question 38

Describe the transformation of y = f(x) for the new function
y = f(x) - 5

Accepted Answer

The graph of y = f(x) was shifted down 5 units.

Answer

The graph of y = f(x) was shifted to the right 5 units.

Answer

The graph of y = f(x) was shifted to the left 5 units.

Answer

The graph of y = f(x) was shifted up 5 units.

Question 39

Describe the transformation of y = f(x) for the new function
y = 5f(x)

Accepted Answer

The graph of y = f(x) was stretched vertically by a factor of 5

Answer

The graph of y = f(x) compressed horizontally by a factor of 1/5

Answer

The graph of y = f(x) was stretched horizontally by a factor of 5

Answer

The graph of y = f(x) was compressed vertically by a factor of 1/5

Question 40

Describe the transformation of y = f(x) for the new function
y = 1/5f(x)

Accepted Answer

The graph of y = f(x) was compressed vertically by a factor of 1/5

Answer

The graph of y = f(x) compressed horizontally by a factor of 1/5

Answer

The graph of y = f(x) was stretched horizontally by a factor of 5

Answer

The graph of y = f(x) was stretched vertically by a factor of 5

Question 41

Describe the transformation of y = f(x) for the new function
y = - f(x)

Accepted Answer

The graph of y = f(x) was flipped vertically across the x axis.

Answer

The graph of y = f(x) was flipped horizontally across the y axis.

Answer

The graph of y = f(x) was shifted down.

Answer

The graph of y = f(x) was shifted up

Question 42

Describe the transformation of y = f(x) for the new function
y = f(- x)

Accepted Answer

The graph of y = f(x) was flipped horizontally across the y axis.

Answer

The graph of y = f(x) was flipped vertically across the x axis.

Answer

The graph of y = f(x) was shifted down.

Answer

The graph of y = f(x) was shifted up

Question 43

Describe the transformation of y = g(x) for the function
y = 3g(x - 3) + 5

Accepted Answer

Shifted up 5 units
Shifted right 3 units
Stretched vertically by a factor of 3

Answer

Shifted up 5 units
Shifted left 3 units
Stretched vertically by a factor of 3

Answer

Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 3

Answer

Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 1/3

Question 44

Identify the transformation from the graph of f(x)=x²to the graph g(x)= x² - 5

Accepted Answer

shifted down five units

Answer

shifted up five units

Answer

shifted left five units

Answer

shifted right five units

Question 45

Identify the transformation from the graph of f(x)=x²to the graph g(x)= (x+5)²

Accepted Answer

shifted left 5 units

Answer

shifted up five units

Answer

shifted down five units

Answer

shifted right 5 units

Question 46

Identify the transformation from the graph of f(x)=x²to the graph g(x)= x² + 5

Accepted Answer

shifted up five units

Answer

shifted down five units

Answer

shifted left five units

Answer

shifted right five units

Question 47

Identify the transformation from the graph of f(x)=x²to the graph g(x)= (x - 5)²

Accepted Answer

shifted right five units

Answer

shifted up five units

Answer

shifted down five units

Answer

shifted left five units

Question 48

Which equation describes the transformation of shifting f(x)=x³ seven units up?

Accepted Answer

x3+7

Answer

x3-7

Answer

(x-7)3

Answer

(x+7)3

Question 49

Which equation describes the transformation of shifting f(x)=x³ four units down?

Accepted Answer

x3- 4

Answer

x3+ 4

Answer

(x - 4)3

Answer

(x + 4)3

Question 50

Which equation describes the transformation of shifting f(x)=x³ two units right?

Accepted Answer

(x - 2)3

Answer

x3 + 2

Answer

x3 - 2

Answer

(x + 2)3

Question 51

Which equation describes the transformation of shifting f(x)=x³ three units left?

Accepted Answer

(x + 3)3

Answer

x3 + 3

Answer

x3 - 3

Answer

(x - 3)3

Question 52

Identify the transformation from the graph of f(x)=2^xto the graph g(x)=2^x-3

Accepted Answer

shifted down three units

Answer

shifted up three units

Answer

shifted left three units

Answer

shifted right four units

Question 53

Question 53.

Accepted Answer

Linear

Answer

Constant

Answer

Exponential

Answer

Quadratic

Question 54

Question 54.

Accepted Answer

y=x

Answer

y=x2

Answer

y=c

Answer

y=|x|

Question 55

Question 55.

Accepted Answer

Quadratic

Answer

Cubic

Answer

Linear

Answer

Exponential

Question 56

Question 56.

Accepted Answer

y=x2

Answer

y=x3

Answer

y=[x]

Answer

y=|x|

Question 57

Question 57.

Accepted Answer

Cubic

Answer

Constant

Answer

Exponential

Answer

Quadratic

Question 58

Question 58.

Accepted Answer

Square Root

Answer

Cube Root

Answer

Exponential

Answer

Rational

Question 59

Question 59.

Accepted Answer

Cube Root

Answer

Square Root

Answer

Exponential

Answer

Cubic

Question 60

Question 60.

Accepted Answer

Absolute Value

Answer

Square Root

Answer

Inverse Squared

Answer

Cubic

Question 61

Question 61.

Accepted Answer

Exponential Growth

Answer

Greatest Integer (Step)

Answer

Logarithm

Answer

Absolute Value

Question 62

This puppet hoped to be a real boy.

Accepted Answer

Pinnochio

Answer

The Hulk

Answer

Roger Rabbit

Answer

John Cena

Question 63

Who does this dog belong to?

Accepted Answer

Mickey Mouse

Answer

Donald Duck

Answer

Minnie Mouse

Answer

John Cena

Question 64

What is the rabbit's name?

Accepted Answer

Thumper

Answer

Bumper

Answer

Bugs

Answer

Jumper

Transformations of Parent Functions

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