Quiz about Transformations

Question 1

f(x) = x² - 6

Accepted Answer

Vertical translation down

Answer

Vertical translation up

Answer

Horizontal translation left

Answer

Horizontal translation right

Answer

Reflection over the x-axis

Question 2

What will be the vertex of

f(x) = 4 (x-3)² + 1 ?

Accepted Answer

(3,1)

Answer

(1,3)

Answer

(-3,1)

Answer

(3, -1)

Answer

None of these.

Question 3

Let the graph of g be a translation 2 units down and 4 units left of the graph of f(x) = x². Write a rule for g.

Accepted Answer

g(x) = (x + 4)² - 2

Answer

g(x) = (x - 4)² - 2

Answer

g(x) = (x - 4)² + 2

Answer

g(x) = (x + 4)² + 2

Question 4

Let the graph of g be a vertical stretch by a factor of 5 of the graph of f(x) = x². Write a rule for g.

Accepted Answer

g(x) = 5x²

Answer

g(x) = -5x²

Answer

g(x) = x² + 5

Answer

g(x) = (x + 5)²

Question 5

Let the graph of g be a translation 7 units right and a reflection in the x-axis of the graph of f(x) = x². Write a rule for g.

Accepted Answer

g(x) = -(x - 7)²

Answer

g(x) = (x - 7)²

Answer

g(x) = -(x + 7)²

Answer

g(x) = (x + 7)²

Question 6

Let the graph of g be a translation 7 units right and 12 units up of the graph of f(x) = (x + 3)²- 8. Write a rule for g.

Accepted Answer

g(x) = (x - 4)²+ 4

Answer

g(x) = (x + 10)²+ 4

Answer

g(x) = (x - 4)²- 20

Answer

g(x) = (x + 10)²- 20

Question 7

Let the graph of g be a reflection in the x-axis of the graph of f(x) = x²- 7. Write a rule for g.

Accepted Answer

g(x) = -x² + 7

Answer

g(x) = x² + 7

Answer

g(x) = -x² - 7

Answer

g(x) = -7x²

Question 8

Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the x-axis of the graph of f(x) = x²+ 2. Write a rule for g.

Accepted Answer

g(x) = -3x²- 6

Answer

g(x) = 3x²+ 6

Answer

g(x) = -3x²- 2

Answer

g(x) = 3x²+ 2

Question 9

For g(x) = (x - 10)²- 4, describe the transformation from the parent function.

Accepted Answer

Shift right 10 and down 4 units

Answer

Shift left 10 and down 4 units

Answer

Shift left 10 and up 4 units

Answer

Shift right 10 and up 4 units

Question 10

For g(x) = 2(x + 3)², describe the transformation from the parent function.

Accepted Answer

Vertical stretch by factor of 2, slide left 3 units

Answer

Vertical stretch by factor of 2, slide right 3 units

Answer

Slide up 2 units and left 3 units

Answer

Slide up 2 units and right 3 units

Question 11

For g(x) = -x²+13, describe the transformation from the parent function.

Accepted Answer

Reflection in x-axis, slide up 13 units

Answer

Reflection in x-axis, slide down 13 units

Answer

Slide up 13 units

Answer

Slide down 13 units

Question 12

For g(x) = -3(x - 6)²+ 2, choose the transformation from the parent function that does NOT occur.

Accepted Answer

Slide 6 units left

Answer

Reflection in the x-axis

Answer

Vertical stretch by factor of 3

Answer

Slide 2 units up

Question 13

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation.

Accepted Answer

g(x) is shifted down 6 units

Answer

g(x) is shifted up 6 units

Answer

g(x) is shifted left 6 units

Answer

g(x) is shifted right 6 units

Question 14

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

Accepted Answer

The graph of g is a vertical translation 2 units up of the graph of f

Answer

The graph of f is a horizontal translation two units left of g

Answer

The graph of g is a vertical stretch by a factor of 2 of the graph of f

Answer

The graph of g is a reflection of the graph of f

Question 15

What is the linear parent function?

Accepted Answer

y = x

Answer

y = mx + b

Answer

f(x) = 2x

Answer

Not here

Question 16

If the graph of the parent function f(x) = x is shifted 7 units
down, which of the following equations would the new graphed
line represent?

Accepted Answer

f(x) = x - 7

Answer

f(x) = 7x

Answer

f(x) = x + 7

Answer

f(x) = 7x - 7

Question 17

Which of the following g(x) equations is vertically stretched and shifted down from f(x) = x?

Accepted Answer

g(x) = 2 f(x) - 6

Answer

g(x) = 2 f(x) + 6

Answer

g(x) = 1/2 f(x) + 6

Answer

g(x) = 1/2 f(x) - 6

Question 18

The linear parent function, f(x) = x, is transformed to g(x) = f(x) + 3. Describe the transformation.

Accepted Answer

g(x) is shifted up 3 units

Answer

g(x) is shifted down 3 units

Answer

g(x) is shifted left 3 units

Answer

g(x) is shifted right 3 units

Question 19

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 20

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

Accepted Answer

Graph g shifted down 4 units

Answer

Graph g shifted down 3 units

Answer

Graph g shifted up 4 units

Answer

Graph g reflected

Question 21

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

Accepted Answer

Graph g shifted up 6 units

Answer

Graph g shifted down 6 units

Answer

Graph g is steeper by a factor of 7

Answer

Graph g is less steep by a factor of 1/3

Question 22

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

Accepted Answer

Graph g reflected and shifted down 2 units.

Answer

Graph g reflected

Answer

Graph g shifted up 2 units

Answer

Graph g reflected and shifted up 2 units

Question 23

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 reflection across the line x = -4

Answer

a reflection across the line y = -4

Answer

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

Question 24

Match the description to its equation.
Moves up 2
Moves left 4

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 25

Match the description to its equation.
Moves right 7

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 26

Match the description to its equation.
Moves down 1
Moves right 1

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 27

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

Accepted Answer

Reflection across the x-axis.

Answer

Nothing happens, it stays the same.

Answer

Vertical stretch by a factor of 2.

Answer

Vertical translation up by 2 units.

Question 28

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

Accepted Answer

Vertical translation up by 2 units.

Answer

Nothing happens, it stays the same.

Answer

Vertical stretch by a factor of 2.

Answer

Reflection across the x-axis.

Question 29

.
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 30

Question 30.

Accepted Answer

g(x)=2x2

Answer

g(x)=0.5x²

Answer

g(x)=x2+2

Answer

g(x)=(x+2)²

Question 31

Which equation describes the transformation of shifting f(x)=x² two units right?

Accepted Answer

(x - 2)2

Answer

x2 + 2

Answer

x2 - 2

Answer

(x + 2)2

Question 32

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 33

The graph shows the function f(x)=x² in blue and another function g(x) in red. Which could be the equation for g(x)?

Accepted Answer

C. g(x) = x² - 3

Answer

A. g(x)=3x²

Answer

B. g(x)=1/3x²

Answer

D. g(x) = (x-3)²

Question 34

If f(x) is the red graph and g(x) is the blue graph, what transformation changes f(x) to g(x)?

Accepted Answer

reflection

Answer

translation

Answer

rotation

Answer

vertical stretch

Question 35

Which function DOES NOT represent a horizontal shift of the function f(x)=x²

Accepted Answer

g(x)= x²+3

Answer

g(x)= (x+3)²

Answer

g(x)= (x-3)²

Answer

g(x) =(x-2)²

Question 36

The linear parent function, f(x) = x, is transformed to g(x) = f(x + 3). Describe the transformation.

Accepted Answer

g(x) is shifted left 3 units

Answer

g(x) is shifted up 3 units

Answer

g(x) is shifted down 3 units

Answer

g(x) is shifted right 3 units

Question 37

Identify the vertex of f(x) = -2(x+1)² + 3

Accepted Answer

(-1,3)

Answer

(h,k)

Answer

(3, 1)

Answer

(-1,-3)

Question 38

What steps transform the graph y = x² to y = 2(x+2)² - 5?

Accepted Answer

Stretch by 2, shifted 2 units left and 5 down

Answer

Compress by 2, shifted 2 units left and 5 down

Answer

Stretch by 5, shifted 5 units left and 2 down

Answer

Compress by 5, shifted 2 units left and 2 down

Question 39

What steps transform the graph y = x² to y = (x-4)²

Accepted Answer

Shifted right 4 units

Answer

Shifted down 4 units

Answer

Shifted left 4 units

Answer

Shifted up 4 units

Question 40

How did we transform from the parent function?
y = x² + 2

Accepted Answer

vertical shift up

Answer

horizontal shift up

Answer

horizontal shift down

Answer

vertical shift down

Question 41

How did we transform from y=x^2?

y = -3x²

Accepted Answer

vertical reflection and vertical stretch

Answer

vertical reflection and vertical shift down

Answer

horizontal stretch

Answer

vertical reflection and vertical compression

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

Transformations

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