2.4 Function Transformations

​2.4 Function Transformations

Part 1 Rigid Transformations​

Some text here about the topic of discussion

Makes new functions​ from parent functions.​

Ex.

Parent :f(x)=x² ​

Transformation: g(x)=a⋅ ​x²

​Some text here about the topic of discussion.

​Transformations:

​

​https://www.desmos.com/calculator/03qhuiciqj

Changes posistion or orientation of a function.

-moves UP or Down

-moves Left or Right

-Reflection across X-axis

-Reflection across Y-axis​

​Rigid

Transformations:

​

​

​f(x)+a moves up by a units

​

f(x)-a moves down​ by a units

​MOve Up or Down

ANY Parent Function​

​Using quadratic and absolute value

​ https://www.desmos.com/calculator/qtujbgppoy

Multiple Choice

Describe the transformation

$$f\left(x\right)+3$$  

• 3 Units Up

• 3 Units Down

• 3 Units Left

• 3 Units Right

Multiple Choice

Describe the transformation

$$f\left(x\right)-6$$  

• 6 Units Up

• 6 Units Down

• 6 Units Left

• 6 Units Right

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

​f(x+a) moves left by a units

​

f(x-a) moves right​ by a units

​MOve left or right

ANY Parent Function​

​Using quadratic and absolute value

​ https://www.desmos.com/calculator/z6azu7enxr

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

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

​-1⋅f(x) reflect over the x-axis

​

f(-1⋅x) reflect over y-axis

​REflect over x or y

ANY Parent Function​

​Using quadratic and absolute value

​ https://www.desmos.com/calculator/klo8ldr5an

Multiple Choice

Describe the transformations

$$-g\left(x\right)+2$$  

• Reflected across the x-axis

  2 Units Up

• Reflected across the x-axis

  2 Units Down

• Reflected across the y-axis

  2 Units Up

• Reflected across the y-axis

  2 Units Down

Multiple Choice

Describe the transformations

$$g\left(-x\right)-4$$  

• Reflected across the x-axis

  4 Units Left

• Reflected across the x-axis

  4 Units Down

• Reflected across the y-axis

  4 Units Left

• Reflected across the y-axis

  4 Units Down

Audio Response

How would you describe the graph of the equation $$g\left(x\right)=\left(x-3\right)^3+2$$  ?

Write out your response before recording yourself.

Open Audio Recorder