Transformations of Parent Functions

Transformations of Parent Functions

Algebra II

Transformation -

happens when the parent function has been shifted left or right OR

shifted up or down OR

stretched or compressed OR

reflected over the x-axis (or y axis)

OR a combination of any of the above.

Fill in the Blanks

Fill in the Blanks

Horizontal Shifting Left and Right

Horizontal translation

Horizontal translation

Multiple Choice

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)?

• A.  g(x) = -x³
• B.  g(x) = x³ - 1
• C.  g(x) = (x + 1)³
• D.  g(x) = (x - 1)³

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

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.

• up 3

• down 3

• left 3

• right 3

Multiple Choice

f(x) = (1/4)^x+3

• Vertical translation up

• Horizontal translation left

• Horizontal translation right

• Vertical compression

• No transformation

Multiple Choice

Which of the following graphs has NOT been shifted horizontally?

Vertical Shifting Up and Down

Vertical translation

Vertical translation

Multiple Choice

f(x) = x² - 6

• Vertical translation up

• Vertical translation down

• Horizontal translation left

• Horizontal translation right

• Reflection over the x-axis

Multiple Choice

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

• Translation left 2 units
• Translation right 2 units
• Vertical translation up by 2 units.
• Reflection across the x-axis.

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

Which of the following transformations have been applied to the function

 $f\left(x\right)=\sqrt{x}-9$  ?

• Right 9

• Left 9

• Up 9

• Down 9

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

Multiple Select

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

• Horizontal translation left

• Horizontal translation right

• Vertical translation up

• Vertical translation down

• Vertical stretch

Shifting Left and Right & Up and Down

Horizontal & Vertical translation

Consider the parent function

undefined 

The graph g(x) is the result when f(x) moves up 1 unit and left 2 units.

The graph h(x) is the result when f(x) moves right 3 units and down 1 unit.

Horizontal & Vertical translation

Consider the parent function

undefined 

The graph g(x) is the result when f(x) moves up 1 unit and left 2 units.

The graph h(x) is the result when f(x) moves right 3 units and down 1 unit.

Multiple Select

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

• Horizontal translation left

• Horizontal translation right

• Vertical translation up

• Vertical translation down

• Vertical stretch

Multiple Choice

Describe the transformation

• left 2 up 5

• right 2 up 5

• left 2 down 5

• right 2 down 5

Multiple Choice

What does the transformation $f\left(x\right)\ =\ f\left(x+1\right)-9$ 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 shifts have occurred?

• left 1, up 5
• left 1, down 5
• right 1, down 5
• right 1, up 5

Multiple Choice

Which graph shows this transformation?

Multiple Choice

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

• (2,-4)
• (-2,4)
• (8,4)
• (-2,-8)

Open Ended

Write the equation of a square root function that has been shifted down 12 units and right 9 units.