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.

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

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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.