Quiz about Transformation of Functions

Question 1

If the blue function is f(x)=x², then the red function 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 2

Match the equation to its description.

Accepted Answer

Right 2 and up 2

Answer

Left 2 and up 2

Answer

Right 2 and down 2

Answer

Left 2 and down 2

Question 3

Identify the coordinates of the point (3 , -2), translated 5 units left and 6 units up.

Accepted Answer

(-2,4)

Answer

(2,-4)

Answer

(8,4)

Answer

(-2,-8)

Question 4

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 5

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

Accepted Answer

shifted right three units

Answer

shifted up three units

Answer

shifted down three units

Answer

shifted left three units

Question 6

Identify the transformation from the graph of f(x)=2^xto the graph g(x)=2^x + 4

Accepted Answer

shifted up four units

Answer

shifted down four units

Answer

shifted left four units

Answer

shifted right four units

Question 7

Identify the transformation from the graph of f(x)=2^xto the graph g(x)=2^(x+4)

Accepted Answer

shifted left four units

Answer

shifted up four units

Answer

shifted down four units

Answer

shifted right four units

Question 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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

Accepted Answer

x3 - 5

Answer

x3 + 5

Answer

(x + 5)3

Answer

(x - 5)3

Question 16

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 17

Give the equation of the graph:

Accepted Answer

y=|x+1|+2

Answer

y=|x+2|+1

Answer

y=|x-2|+1

Answer

y=|x-1|+2

Question 18

Give the equation of the graph:

Accepted Answer

y=-|x-1|+3

Answer

y=|x-1|+3

Answer

y=|x+3|+1

Answer

y=-|x+3|+1

Question 19

Describe the graph of y=(x+3)²-7

Accepted Answer

The quadratic, moved 3 left and 7 down

Answer

The quadratic, moved 3 right and 7 down

Answer

The quadratic, moved 7 right and 3 down

Answer

The quadratic, moved 7 left and 3 up

Question 20

Describe the graph of y=(x-4)³+2

Accepted Answer

The cubic, moved 4 right and 2 up.

Answer

The quadratic, moved 4 right and 2 up.

Answer

The cubic, moved 4 left and 2 up.

Answer

The absolute value, moved 4 right and 2 up.

Question 21

Find the equation of a quadratic moved 5 right and 3 down.

Accepted Answer

y=(x-5)²-3

Answer

y=(x+3)²+5

Answer

y=(x+5)²-3

Answer

y=(x-3)²-5

Question 22

How did the equation shift from the parent function? y=x+7

Accepted Answer

Up 7

Answer

Down 7

Answer

Flipped

Answer

Steeper

Question 23

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 24

f(x) = 5x² + 2

Accepted Answer

Stretch of 5
Up 2

Answer

Shrink of 5
Up 2

Answer

Stretch of 5
Down 2

Answer

Shrink of 5
Down 2

Question 25

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 26

How did we transform from the parent function?
y = -1/2(x - 1)² + 3

Accepted Answer

reflection, vertical compression, horizontal right, vertical up

Answer

vertical compression, horizontal shift left, vertical shift up

Answer

reflection, horizontal shift right, vertical shift down

Answer

no changes were made to y = x²

Question 27

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 28

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

Answer

f(x) =  I x - 2 I

Question 29

Which equation shows a function that is translated left 4 and 7 up?

Accepted Answer

y = |x + 4| + 7

Answer

y = (x - 4)² + 7

Answer

y = (x + 7)² - 4

Answer

y = |x + 4| - 7

Question 30

Which equation shows a function with a vertical shift up from the parent function?

Accepted Answer

y = x² + 1

Answer

y = |x + 6|

Answer

y = |x| - 2 + 1

Answer

y = x² + 7 - 9

Question 31

What transformation happens to the function f(x) = x² + 3 ?

Accepted Answer

Shifts 3 up

Answer

Shifts 3 down

Answer

Shifts 3 left

Answer

Shifts 3 right

Question 32

What transformation happens to the function f(x) = |x| - 5 ?

Accepted Answer

Shifts down 5

Answer

Shifts up 5

Answer

Shifts right 5

Answer

Shifts left 5

Question 33

What type of function is g(x) = x² - 6

Accepted Answer

Quadratic

Answer

Square root

Answer

Linear

Answer

Absolute Value

Question 34

What transformations happen to the function g(x) = (x + 2)² + 7 ?

Accepted Answer

2 left, 7 up

Answer

2 right, 7 up

Answer

2 up, 7 right

Answer

2 down, 7 right

Question 35

What transformations happen to the function g(x) = (x + 2)² + 7 ?

Accepted Answer

2 left, 7 up

Answer

2 right, 7 up

Answer

2 up, 7 right

Answer

2 down, 7 right

Question 36

What transformations happen to the function h(x) = |x - 4| - 2 ?

Accepted Answer

4 left, 2 down

Answer

4 up, 2 left

Answer

4 right, 2 down

Answer

4 down, 2 right

Question 37

What transformations happen to the function f(x) = - x² + 5

Accepted Answer

Reflect, up 5

Answer

Reflect, right 5

Answer

Stretch, up 5

Answer

Shrink, right 5

Question 38

What transformations happen to the function g(x) = (x + 6)² - 4 ?

Accepted Answer

6 left, 4 down

Answer

6 right, 4 down

Answer

6 down, 4 right

Answer

6 up, 4 left

Question 39

What transformation happens to the function g(x) = 3|x| ?

Accepted Answer

Stretch by 3

Answer

Shrink by 3

Answer

Left 3

Answer

Up 3

Question 40

What transformations happen to the function f(x) = -|x + 4| ?

Accepted Answer

Reflect, left 4

Answer

Reflect, right 4

Answer

Reflect, down 4

Answer

Shrink, right 4

Question 41

What transformations happen to the function h(x) = -1/4 |x  - 8| ?

Accepted Answer

Reflect, shrink 1/4, right 8

Answer

Reflect, down 8

Answer

Reflect, stretch 1/4, up 8

Answer

Reflect, shrink 1/4, left 8

Question 42

What transformations happen to the function f(x) = -3(x - 4)² ?

Accepted Answer

reflect, stretch 3, right 4

Answer

left 3, down 4

Answer

reflect, stretch 3, left 4

Answer

down 3, right 4

Question 43

What type of function is shown?

Accepted Answer

exponential

Answer

logarithm

Answer

quadratic

Answer

square root

Question 44

What type of function is shown?

Accepted Answer

linear

Answer

absolute value

Answer

quadratic

Answer

exponential

Question 45

What type of function is shown?

Accepted Answer

absolute value

Answer

linear

Answer

quadratic

Answer

square root

Question 46

What is the equation of this graph?

Accepted Answer

f(x) = |x + 2| - 3

Answer

f(x) = (x + 2)² - 3

Answer

f(x) = (x - 2)² - 3

Answer

f(x) = |x - 2| - 3

Question 47

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 48

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 49

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

Transformation of Functions

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