Lesson 3 Transformations of Cubic and Cube root functions

We will analyze transformations to cubic and cube root functions.
I will summarize transformations to both cubic and cube root functions.
2A.6A

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Cubic and Cube root Transformations

Dropdown

x-intercept: ​

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y-intercept: ​

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Domain & Range: ​

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Min/Max:​

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Word Cloud

Summarize in one word what we LOOKED at in Lessons 1 and 2...

The parent functions pictured above, before any transformations have been applied!

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Parent Functions

Match

Match the following graphs/information to their equations.

Both functions

• $$f(x)=x^3$$

• $$f(x)=\sqrt[3]{x}$$

• Both functions

The table shows where INSIDE the function, each transformation happens and what the value does to the corresponding graph.

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Transformations applied

Labeling

Label the image with the correct descriptions that correspond to what you would want to change in the graph. If I wanted the graph to...

Drag labels to their correct position on the image

Flip Horizontally

Move left

Flip vertically

Move down

​Fill in your notes for these examples :)

​Fill in your notes for these examples :)

​Fill in your notes for these examples :)

Open Ended

Comparing the two functions side by side, are the transformations different? Why or why not?

​Fill in your notes for these examples :)

​Fill in your notes for these examples :)

Fill in the Blanks

For example 5: a= b= c= d= (enter in order, no spaces, and separated with commas)

​Fill in your notes for these examples :)

​Fill in your notes for these examples :)

Multiple Choice

The correct equation for example 7 is...

• $$f\left(x\right)=-3\left(x-5\right)^3-7$$

• $$f\left(x\right)=\left(-3x-5\right)^3-7$$

• $$f\left(x\right)=-3\left(x+5\right)^3-7$$

• $$f\left(x\right)=\left(-3x+5\right)^3-7$$

​Fill in your notes for these examples :)

​Fill in your notes for these examples :)

Multiple Choice

The correct equation for example 8 is...

• $$f\left(x\right)=\frac{2}{3}\sqrt[3]{-\left(x+5\right)}+1$$

• $$f\left(x\right)=-\frac{2}{3}\sqrt[3]{x+5}+1$$

• $$f\left(x\right)=\frac{2}{3}\sqrt[3]{-\left(x-5\right)}+1$$

• $$f\left(x\right)=\frac{2}{3}\sqrt[3]{-\left(x+5\right)}-1$$

​Fill in your notes for these examples :)

Poll

On a scale of 1-5, how comfortable are you with Transformations?

• 5 - Totally agree I can replicate this in my sleep

• 4 - I am confident I understand this

• 3 - I might need some more practice but overall feel good

• 2 - I definitely need more practice and maybe some clarification...

• 1 - Help... I'm lost :(