2.4 Parent Function Transformations 2

​2.4 Parent FUnction Transformations

Part 2: NON-Rigid Transformations​

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Some text here about the topic of discussion

​Change the shape of a function by changing its size, i.e. thinner, fatter, shorter, longer.​

Dilations ​are non-rigid transformations.

Compress (shorter/fatter) and stretch (thinner, longer)​

Non-Rigid Transfomations

a⋅​f(x)

​if a> 1 Stretches by a factor of a.

​

if a<1 Compresses by a factor of a.

​Vertical DIlations

on all Functions​

​ https://www.desmos.com/calculator/jb3enfbows

Multiple Choice

Describe the transformation from the parent quadratic function:

$$y=\frac{1}{4}x^2$$  

• Vertical stretch by a factor of ¼

• Vertical shrink by a factor of ¼

Multiple Choice

Describe the transformation from the parent absolute value function:

$$y=8\left|x\right|$$  

• Vertical stretch by a factor of 8 

• Vertical shrink by a factor of 8 

Fill in the Blanks

Write the equation for an absolute value function stretched by a factor of 4 vertically.

Multiple Choice

What steps transform the graph  $$y=x^2$$   to  $$y=-\frac{1}{2}\left(x-4\right)^2+1$$ ?

• Compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

• Stretched by 1/2, shifted 4 units right and 1 unit down

​f(a⋅x)

​if a> 1 Stretches

​

if a<1 Compresses

Horizontal DIlations

on all Functions​

​ https://www.desmos.com/calculator/bh31nsts96

Fill in the Blanks

Write the equation of a absolute value function horizontally compressed by 0.5.

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 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

Audio Response

Describe the transformations on the function from $$f\left(x\right)=\sqrt[]{x}$$   to $$f\left(x\right)=2\sqrt[3]{3x}-1$$  . Write out the discription before recording it.

Open Audio Recorder