Functions and Transformations

Functions and Transformations

Multiple Choice

Describe the transformation from the parent absolute value function:

$$y=\left|x\right|-5$$  

• Shift up 5 units

• Shift down 5 units

• Shift right 5 units

• Shift left 5 units

Multiple Choice

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

• y = x² + 5
• y = (x + 5)²
• y = 5x²
• y = -x² - 5

Multiple Choice

Describe the transformation from the parent quadratic function:

$$y=\left(x-2\right)^2$$  

• Shift up 2 units

• Shift down 2 units

• Shift right 2 units

• Shift left 2 units

Multiple Choice

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

• y = x² + 4
• y = (x + 4)²
• y = (x - 4)²
• y = 4x²

Multiple Choice

Describe the transformation from the parent square root function:

$$y=\sqrt[]{x+4}$$  

• Shift up 4 units

• Shift down 4 units

• Shift right 4 units

• Shift left 4 units

Multiple Choice

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

• y = x² + 2
• y = -x² + 2
• y = x² - 2
• y = -(x + 2)²

Multiple Select

Describe the transformation from the parent cubic function:

$$y=-x^3+3$$  

* Select TWO answers *

• Shift up 3 units

• Shift down 3 units

• Reflection over the y-axis

• Reflection over the x-axis

Multiple Choice

Describe the transformations from the original parent function f(x) = x².

g(x) = 5x² + 2

• Vertical Stretch of 5

  Vertical Down 2

• Vertical Compression of 5

  Vertical Up 2

• Vertical Stretch of 5

  Vertical Up 2

• Vertical Compression of 5

  Vertical Down 2

Multiple Choice

Describe the transformation from the parent quadratic function:

$$y=\frac{1}{4}x^2$$  

• Vertical stretch by a factor of ¼

• Vertical compression by a factor of ¼

Multiple Choice

What are the transformations of this functions compared to the parent function y = √(x)?

• Horizontal right 5, vertical down 2, and reflected over the x-axis

• Reflected over the x-axis, vertical stretch of 2, and horizontal right 5

• Reflected over the x-axis, vertical stretch of -2, and horizontal left 5

• Horizontal right 5, Vertical down 2

Multiple Choice

Describe the transformation from the parent absolute value function:

$$y=8\left|x\right|$$  

• Vertical stretch by a factor of 8 

• Vertical compression by a factor of 8 

Multiple Choice

The parent function is $$x^3$$

• f(x) = −(x−2)³−1
• f(x) = −(x+2)³−1
• f(x) = −(x−2)³ + 1
• f(x) = −(x+2)³ + 1

Multiple Select

Describe the transformation from the parent square root function:

$$y=2\ \sqrt[]{x-5}$$  

* Select TWO answers *

• Vertical stretch

• Vertical compression

• Translation 5 units right

• Translation 5 units left

Multiple Choice

What is the equation of this graph?

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

Multiple Select

Describe the transformation from the parent absolute value function:

$$y=-\left|x+4\right|-3$$  

* Select THREE answers *

• Reflection over the x-axis

• Translation 4 units left

• Translation 4 units up

• Translation 3 units left

• Translation 3 units down

Multiple Choice

What is the equation of the graph? The parent function is $$\sqrt[]{x}$$

• y = √(x - 3)
• y = √(x) + 3
• y = √(x - 5) + 4
• y = √(x + 5) + 4

Multiple Select

Describe the transformation from the parent cubic function:

$$y=\left(x+6\right)^3-4$$  

* Select TWO answers *

• Translation 6 units right

• Translation 6 units left

• Translation 4 units up

• Translation 4 units down

Multiple Choice

Which equation represents this graph.

• f(x)=(x - 4)² - 3
• f(x)=-(x - 4)² + 3
• f(x)=(x - 4)² + 3
• f(x)=-(x + 4)² + 3

Multiple Choice

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

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

Multiple Choice

Describe the transformation

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Multiple Choice

What is the equation of this graph? Remember that the parent function of $$\left|x\right|$$

• f(x) = 2(x + 2)² - 3

• f(x) = 2(x - 2)² - 3

• f(x) =2|x + 2| - 3

• f(x) = 2|x - 2| - 3

Multiple Choice

Which parent function matches the graph?

• y = |x|
• y = x
• y = x²
• y = 2^x

Multiple Choice

What type of function is shown?

• absolute value
• quadratic
• linear
• exponential

Multiple Choice

What type of function is shown?

• linear
• quadratic
• square root
• absolute value

Multiple Choice

Name the parent function. 

• constant
• square root
• linear
• absolute value

Multiple Choice

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

• y = x² + 5
• y = (x + 5)²
• y = 5x²
• y = -x² - 5

Multiple Choice

What type of function is shown?

• cube root
• square root
• logarithm
• exponential

Multiple Choice

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

• y = x² + 4
• y = (x + 4)²
• y = (x - 4)²
• y = 4x²

Multiple Choice

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

• y = x² + 2
• y = -x² + 2
• y = x² - 2
• y = -(x + 2)²

Multiple Choice

Describe the transformation

• left 2 up 5
• right 2 up 5
• left 2 down 5
• right 2 down 5

Multiple Choice

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

• y = |x - 5|
• y = |x + 5|
• y = |x| + 5
• y = -5|x|

Multiple Choice

Tell how the graph transformed.
y = (x - 3)²

• Translated right 3
• Translated left 3
• Translated up 3
• Translated down 9

Multiple Choice

Describe the transformation.

• up 3

• down 3

• left 3

• right 3

Multiple Choice

Given the function $$y=\left(x+4\right)^2+2$$  , what is the parent function?

• $$y=x^2$$  

• $$y=a\left(x-h\right)^2+k$$  

• $$y=mx+b$$  

• $$y=0\left(x-0\right)^2+0$$  

Multiple Choice

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

• $$y=-\left|x-15\right|-3$$

• $$y=-\left|x+15\right|-3$$

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

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

• $$y=\left|-x-15\right|-3$$

Multiple Choice

What does the transformation $$f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$$ do to the graph of  $$f\left(x\right)$$  ?

• translates it left one unit and down 9 units

• translates it right one unit and down 9 units

• translates it up one unit and right 9 units

• translates it down one unit and left 9 units

Multiple Choice

What is the equation to this graph?

• f(x)= Ix+2I +1
• f(x)= Ix-2I +1
• f(x)= Ix+2I -1
• f(x)= Ix-2I -1

Multiple Choice

Name the parent function.

• linear
• exponential
• logarithmic
• cubic

Multiple Choice

what is the transformation?

• horizontal shift to the right 2 and vertical shift up 4
• horizontal shift to the right 2 and vertical shift down 4
• horizontal shift to the left 2 and vertical shift up 2
• horizontal shift to the left 2 and vertical shift down 2

Multiple Choice

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

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²