Quiz about Functions & Transformations

Question 1

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 2

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 3

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 4

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 5

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 6

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 7

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 8

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 9

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 10

.
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 11

.
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 12

What are the following transformations?
- f(x+2)

Accepted Answer

reflection over the x axis and 2 units left

Answer

reflection over the y axis and 2 units to the right

Answer

reflection over the x axis and 2 units right

Answer

reflection over the y axis and 2 units left

Question 13

What are the following transformations:
f(-x) - 4

Accepted Answer

reflection over the y axis and 4 units down

Answer

reflection over the x axis and 4 units right

Answer

reflection over the x axis and 4 units down

Answer

reflection over the y axis and 4 units right

Question 14

Which of the following transformations are present?
-2f(x - 1) + 2

Accepted Answer

Shift 1 unit right

Answer

Shift 1 unit down

Answer

Shift 1 unit up

Answer

Shift 1 unit left

Question 15

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 16

Which equation represents this graph.

Accepted Answer

f(x)=-(x - 4)² + 3

Answer

f(x)=(x - 4)² - 3

Answer

f(x)=(x - 4)² + 3

Answer

f(x)=-(x + 4)² + 3

Question 17

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 18

Which transformation will occur when $g\left(x\right)=2f\left(x\right)$ ?

Accepted Answer

Vertical stretch by a factor of 2

Answer

Vertical compression by a factor of 1/2

Answer

Horizontal stretch by a factor of 2

Answer

Horizontal compression by a factor of 1/2

Question 19

What does the transformation $g\left(x\right)\ =\ f\left(x+1\right)$ do to the graph of $f\left(x\right)$ ?

Accepted Answer

translates it left one unit

Answer

translates it right one unit

Answer

translates it up one unit

Answer

translates it down one unit

Question 20

Question 20.

Accepted Answer

No, "+3" on the end of the function moves the function to the up 3 units

Answer

Yes, "+3" on the end of the function moves the function to the right 3 units

Answer

No, "+3" on the end of the function moves the function to the left 3 units

Answer

No, "+3" on the end of the function moves the function to the down 3 units

Question 21

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 22

Which equation is an absolute value graph shifted right 5 units?

Accepted Answer

y = |x - 5|

Answer

y = |x + 5|

Answer

y = |x| + 5

Answer

y = -5|x|

Question 23

Question 23.

Accepted Answer

y = -Ix + 2I - 1

Answer

y = Ix + 2I - 1

Answer

y = -Ix - 2I - 1

Answer

y = -Ix + 1I - 2

Question 24

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 25

Describe the transformation from the parent graph

Accepted Answer

Reflect over x, right 3, down 4

Answer

Reflect over y, right 3, down 4

Answer

Reflect over x, right 3, up 4

Answer

Reflect over y, left 3, down 4

Question 26

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 27

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 28

What type of function is shown?

Accepted Answer

square root

Answer

cube root

Answer

logarithm

Answer

exponential

Question 29

What type of function is shown?

Accepted Answer

absolute value

Answer

linear

Answer

quadratic

Answer

square root

Question 30

What is the equation of the PARENT  function?

Accepted Answer

f(x) = x3

Answer

f(x) = 2x

Answer

f(x) = |x|

Answer

f(x) = x

Question 31

Which parent function matches the graph?

Accepted Answer

y = x2

Answer

y = |x|

Answer

y = x

Answer

y = 2x

Question 32

What type of function is shown?

Accepted Answer

linear

Answer

absolute value

Answer

quadratic

Answer

exponential

Question 33

What type of function is shown?

Accepted Answer

absolute value

Answer

linear

Answer

quadratic

Answer

square root

Question 34

Name the parent function.

Accepted Answer

cubic

Answer

linear

Answer

quadratic

Answer

cube root

Question 35

Name the parent function.

Accepted Answer

absolute value

Answer

constant

Answer

square root

Answer

linear

Question 36

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 37

What type of function is shown?

Accepted Answer

square root

Answer

cube root

Answer

logarithm

Answer

exponential

Question 38

What family does the pictured graph belong to?

Accepted Answer

Square root

Answer

Linear

Answer

Quadratic

Answer

Absolute value

Question 39

Which of the following graphs is the Parent Function in the Quadratic Family?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 40

Which of the following graphs shows a "Reflection about the x-axis" from it's Parent Function?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 41

Which of the following graphs has the greatest Vertical Stretch?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 42

Based on the graph, determine the function in the blue. (Hint: it includes all 4 kinds of translation)

Accepted Answer

y = -2( x - 2 )² - 1

Answer

y = -.5( x - 2 )² - 1

Answer

y = -2( x + 2 )² - 1

Answer

y = -2( x - 2 )² + 1

Question 43

Question 43.

Accepted Answer

horizontal shift to the left 4 and vertical shift down 2

Answer

horizontal shift to the right 4 and vertical shift down 2

Answer

horizontal shift to the left 4 and vertical shift up 2

Answer

horizontal shift to the right 4 and vertical shift up 2

Question 44

Question 44.

Accepted Answer

horizontal shift to the right 2 and vertical shift down 4

Answer

horizontal shift to the right 2 and vertical shift up 4

Answer

horizontal shift to the left 2 and vertical shift up 2

Answer

horizontal shift to the left 2 and vertical shift down 2

Question 45

Question 45.

Accepted Answer

horizontal shift to the right 2 and vertical stretch by a factor of 3

Answer

horizontal shift to the left 2 and vertical stretch by a factor of 3

Answer

horizontal shift to the right 2 and vertical compression by a factor of 3

Answer

horizontal shift to the left 2 and vertical compression by a factor of 3

Question 46

If x=2 What is y?

Accepted Answer

y=1

Answer

y= -3

Answer

y= -6

Answer

y= 2

Question 47

If x is -8, what is y?

Accepted Answer

y = 9

Answer

y = -21

Answer

y = 1

Answer

y = 10

Question 48

f(x) = 2^x-1 + 3 (Select ALL that apply!)

Accepted Answer

Horizontal translation right

Accepted Answer

Vertical translation up

Answer

Horizontal translation left

Answer

Vertical translation down

Answer

Vertical stretch

Functions & Transformations

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics