3.6 - Transformations of Functions (Translations)

By Julie Many

Categorize

Options (8)

Categorize the graphs below according to their parent function.

Quadratic Function

Cubic Function

Absolute Value Function

Square Root Function

Multiple Choice

What is the parent function of: $$f\left(x\right)=\left(x+5\right)^2-1$$

• Quadratic
  $$f\left(x\right)=x^2$$

• Cubic

  $$f\left(x\right)=x^3$$

• Absolute Value

  $$f\left(x\right)=\left|x\right|$$

• Square Root

  $$f\left(x\right)=\sqrt[]{x}$$

Open Ended

Describe the transformations (horizontal & vertical shifts):

$$f\left(x\right)=\left(x+5\right)^2-1$$

Multiple Choice

What is the parent function of: $$f\left(x\right)=\sqrt[]{x-1}+4$$

• Quadratic
  $$f\left(x\right)=x^2$$

• Cubic

  $$f\left(x\right)=x^3$$

• Absolute Value

  $$f\left(x\right)=\left|x\right|$$

• Square Root

  $$f\left(x\right)=\sqrt[]{x}$$

Open Ended

Describe the transformations (horizontal & vertical shifts):

$$f\left(x\right)=\sqrt[]{x-1}+4$$

Multiple Choice

What is the parent function of: $$f\left(x\right)=\left(x-5\right)^3+4$$

• Quadratic
  $$f\left(x\right)=x^2$$

• Cubic

  $$f\left(x\right)=x^3$$

• Absolute Value

  $$f\left(x\right)=\left|x\right|$$

• Square Root

  $$f\left(x\right)=\sqrt[]{x}$$

Open Ended

Describe the transformations (horizontal and vertical shifts):

$$f\left(x\right)=\left(x-5\right)^3+4$$

Multiple Choice

What is the parent function of: $$f\left(x\right)=\left|x-2\right|+6$$

• Quadratic
  $$f\left(x\right)=x^2$$

• Cubic

  $$f\left(x\right)=x^3$$

• Absolute Value

  $$f\left(x\right)=\left|x\right|$$

• Square Root

  $$f\left(x\right)=\sqrt[]{x}$$

Open Ended

Describe the transformations (horizontal and vertical shifts):

$$f\left(x\right)=\left|x-2\right|+6$$

Graphing

Plot the new points for the function:

$$f\left(x\right)=\left(x+5\right)^2+3$$

Graphing

Plot the new points for the function:

$$f\left(x\right)=\sqrt[]{x+3}+1$$

Graphing

Plot the new points for the function:

$$f\left(x\right)=\left(x-5\right)^3+4$$