Quiz about Transformations Review

Question 1

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

Accepted Answer

Vertical translation up by 2 units.

Answer

Translation left 2 units

Answer

Translation right 2 units

Answer

Reflection across the x-axis.

Question 2

Which transformation on

f(x) = x

is g(x) = -f(x)

Accepted Answer

Reflection across the x-axis.

Answer

Reflection across the y-axis

Answer

The slope will be less steep

Answer

The graph will be wider

Question 3

Describe the transformation of y = (x - 4)²

Accepted Answer

Shift RIGHT

Answer

Shift UP

Answer

Shift DOWN

Answer

Shift LEFT

Question 4

If the blue is f(x)=x^2,the red must be

Accepted Answer

g(x)=(x-3)²

Answer

g(x)=(x+3)²

Answer

g(x)=x2+3

Answer

g(x)=x2-2

Question 5

Which of the following is the correct equation for the given graph?

Accepted Answer

f(x) = (x + 2)² - 1

Answer

f(x) = (x - 2)² - 1

Answer

f(x) = -(x + 2)² - 1

Answer

f(x) = -(x - 2)² - 1

Question 6

Which of the following is the correct equation for the given graph?

Accepted Answer

f(x) = -3(x - 2)² - 4

Answer

f(x) = -(x + 2)² - 4

Answer

f(x) = -(x - 2)² - 4

Answer

f(x) = -3(x + 2)² - 4

Question 7

What are the transformations of this functions compared to the parent function?

Accepted Answer

Shifted left 2

Answer

Shifted down 2

Answer

Shifted up 2

Answer

Shifted right 2

Question 8

What type of function is shown?

Accepted Answer

square root

Answer

cube root

Answer

logarithm

Answer

exponential

Question 9

What is the equation of the graph below?

Accepted Answer

f(x) = I x - 2 I

Answer

f(x) = I x + 2 I

Answer

f(x) = I x + 2 I +2

Answer

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

Question 10

What is the equation of the graph below?

Accepted Answer

f(x ) = -I x + 4 I + 2

Answer

f(x ) = I x + 4 I + 2

Answer

f(x ) = -I x - 4 I + 2

Answer

f(x ) = I x - 4 I + 2

Question 11

What shifts have occurred?

Accepted Answer

right 1, up 5

Answer

left 1, up 5

Answer

left 1, down 5

Answer

right 1, down 5

Question 12

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

Accepted Answer

y = -|x - 2| - 7

Answer

y = -|x + 2| - 7

Answer

y = |x - 2| - 7

Answer

y = -|x - 2| + 7

Question 13

Name the parent function.

Accepted Answer

cubic

Answer

linear

Answer

quadratic

Answer

cube root

Question 14

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)?

Accepted Answer

D. g(x) = (x - 1)³

Answer

A. g(x) = -x³

Answer

B. g(x) = x³ - 1

Answer

C. g(x) = (x + 1)³

Question 15

What transformations has the function undergone?

Accepted Answer

reflect over x, vertical stretch by 2, right 5, up 1

Answer

reflect over y, vertical compress by 2, right 5, up 1

Answer

reflect over x, horizontal compression by 2, left 5, up 1

Answer

reflect over y, horizontal stretch by -2, right 5, up 1

Question 16

Describe the transformation of the graph
y = -(x - 4)³ + 5

Accepted Answer

Reflect x-axis, Right 4, Up 5

Answer

Up 5 and Left 4

Answer

Reflect x-axis, Left 4, Up 5

Answer

Right 4 and up 5

Question 17

Identify the transformations to the step function:

Accepted Answer

x-axis reflection; stretch of 2; right 2; down 2

Answer

x-axis reflection; stretch of 2; left 2; down 2

Answer

x-axis reflection; shrink of 2; left 2; up 2

Answer

shrink of -2; right 2; down 2

Question 18

What is the name of the parent function?

Accepted Answer

Linear

Answer

Quadratic

Answer

Cubic

Answer

Constant

Question 19

What is the name of the parent function?

Accepted Answer

Absolute Value

Answer

Square Root

Answer

Linear

Answer

Cubic

Question 20

What is the name of the parent function?

Accepted Answer

Quadratic

Answer

Constant

Answer

Square Root

Answer

Linear

Question 21

What is the name of the parent function?

Accepted Answer

Square Root

Answer

Cube Root

Answer

Linear

Answer

Quadratic

Question 22

What is the name of the parent function?

Accepted Answer

Cubic

Answer

Square Root

Answer

Constant

Answer

Absolute Value

Question 23

What is the name of the parent function?

Accepted Answer

Cube Root

Answer

Linear

Answer

Square Root

Answer

Quadratic

Question 24

Linear

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 25

Absolute Value

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 26

Quadratic

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 27

Square Root

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 28

Cubic

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 29

Cube Root

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 30

Which equation below is a quadratic function translated up 5 units?

Accepted Answer

y = x² + 5

Answer

y = (x + 5)²

Answer

y = 5x2

Answer

y = -x² - 5

Question 31

Which equation below is a quadratic function translated left 4 units?

Accepted Answer

y = (x + 4)²

Answer

y = x² + 4

Answer

y = (x - 4)²

Answer

y = 4x2

Question 32

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

Accepted Answer

y = -x² + 2

Answer

y = x² + 2

Answer

y = x² - 2

Answer

y = -(x + 2)²

Question 33

Describe the transformation

Accepted Answer

right 2 up 5

Answer

left 2 up 5

Answer

left 2 down 5

Answer

right 2 down 5

Question 34

Tell how the function transformed from y =|x|
y = -2|x|

Accepted Answer

Stretched vertically and reflected over x-axis

Answer

Translated left 2 units

Answer

Reflected over x-axis

Answer

Compressed vertically and reflected over the x-axis

Question 35

Question 35.

Accepted Answer

y = -Ix + 2I - 1

Answer

y = Ix + 2I - 1

Answer

y = -Ix - 2I - 1

Answer

y = -Ix + 1I - 2

Question 36

What are the transformations to the graph compared to the parent function?

Accepted Answer

Shifted right 2, shifted up 3, and reflected over the x-axis

Answer

Shifted right 2, shifted up 3, and reflected over the y-axis

Answer

Shifted left 2, shifted up 3, and reflected over the y-axis

Answer

Shifted left 2, shifted up 3, and reflected over the x-axis

Question 37

Describe the transformations from the original parent function f(x) = x².
g(x) = 5x² + 2

Accepted Answer

Vertical Stretch of 5
Up 2

Answer

Vertical Stretch of 5
Down 2

Answer

Vertical Shrink of 5
Up 2

Answer

Vertical Shrink of 5
Down 2

Question 38

Describe the parent graph transformation

Accepted Answer

compression by 1/2, left 1, down 3

Answer

stretch by 1/2, left 1, down 3

Answer

stretch by 1/2, right 1, down 3

Answer

compression by 1/2, right 1, down 3

Question 39

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

Accepted Answer

Vertical translation up by 2 units.

Answer

Translation left 2 units

Answer

Translation right 2 units

Answer

Reflection across the x-axis.

Question 40

Which transformation on

f(x) = x

is g(x) = -f(x)

Accepted Answer

Reflection across the x-axis.

Answer

Reflection across the y-axis

Answer

The slope will be less steep

Answer

The graph will be wider

Question 41

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?

Accepted Answer

-f(1/2x) - 4

Answer

f(-2x - 4)

Answer

f(-1/2x) - 4

Answer

-f(2x) - 4

Question 42

If the blue is f(x)=x^2,the red must be

Accepted Answer

g(x)=(x-3)²

Answer

g(x)=(x+3)²

Answer

g(x)=x2+3

Answer

g(x)=x2-2

Question 43

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

Accepted Answer

y = -|x - 2| - 7

Answer

y = -|x + 2| - 7

Answer

y = |x - 2| - 7

Answer

y = -|x - 2| + 7

Question 44

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)?

Accepted Answer

D. g(x) = (x - 1)³

Answer

A. g(x) = -x³

Answer

B. g(x) = x³ - 1

Answer

C. g(x) = (x + 1)³

Question 45

Identify the transformations to the step function:

Accepted Answer

x-axis reflection; stretch of 2; right 2; down 2

Answer

x-axis reflection; stretch of 2; left 2; down 2

Answer

x-axis reflection; shrink of 2; left 2; up 2

Answer

shrink of -2; right 2; down 2

Question 46

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

Accepted Answer

$$y=-\left|x-15\right|-3$$

Answer

$$y=-\left|x+15\right|-3$$

Answer

$$y=\frac{1}{2}\left|x+3\right|-15$$

Answer

$$y=\frac{1}{2}\left|x-3\right|-15$$

Answer

$$y=\left|-x-15\right|-3$$

Question 47

Which transformations are involved in the equation $$y=\frac{1}{2}\sqrt{x+1}-1$$ ?

Accepted Answer

Vertical shrink

Accepted Answer

Horizontal translation left

Accepted Answer

Vertical translation down

Answer

Horizontal translation right

Answer

Vertical stretch

Question 48

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

Accepted Answer

Vertical translation up by 2 units.

Answer

Translation left 2 units

Answer

Translation right 2 units

Answer

Reflection across the x-axis.

Transformations Review

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