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Transformations. Mr. Markwalter. Homecoming. New Starting this Week…. I have noticed that some people are really only choosing to study seriously when a test comes close. We are going to start quizzes every Friday! Here’s the thing, they are open notes and homework!

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Transformations

Transformations

Mr. Markwalter



New starting this week
New Starting this Week…

  • I have noticed that some people are really only choosing to study seriously when a test comes close.

  • We are going to start quizzes every Friday!

  • Here’s the thing, they are open notes and homework!

  • It can really bring your grade up or it can really hurt you.


Before we continue
Before We Continue

  • We need to make sure that we have the right vocab to talk about our next topic.

  • So today we look at…



Transformations2
Transformations

  • Transformations change parent (simple) functions.

  • Let’s take a look at the absolute value function.


Transformations3
Transformations

  • What does absolute value do?


Transformations4
Transformations

  • In groups of no more than three…

  • Graph the functions in this packet and write your conclusions when asked.

  • We will use this to identify our vocabulary for today!

  • It can also be your notes on this topic!



Translations
Translations!

  • If we add a number outside of the original function:

  • VERTICAL TRANSLATION

  • f(x)=x2+1

  • f(x)=2x-1


Translations1
Translations!

  • If we add a number outside of the original function:

  • VERTICAL TRANSLATION (+ up, - down)

  • f(x)=x2+1

  • f(x)=2x-1



Translations2
Translations!

  • If we add a number INSIDE of the original function:

  • HORIZONTAL TRANSLATION (positive left, negative right)

  • f(x)=(x-1)2

  • f(x)=2x+1


Translations3
Translations!

  • If we add a number INSIDE of the original function:

  • HORIZONTAL TRANSLATION (+ left, - right)

  • f(x)=(x-1)2

  • f(x)=2x+1



Reflections
Reflections!

  • If we multiply by a negative OUTSIDE the original function:

  • VERTICAL Reflection across x-axis

  • f(x)=-x2

  • f(x)=-2x


Reflections1
Reflections!

  • If we multiply by a negative OUTSIDE the original function:

  • VERTICAL Reflection across y-axis

  • f(x)=-x2

  • f(x)=-2x



Reflections2
Reflections!

  • If we multiply the x by a negative:

  • HORIZONTAL Reflection across y-axis

  • f(x)=(-x)2

  • f(x)=2-x


Reflections3
Reflections!

  • If we multiply the x by a negative:

  • HORIZONTAL Reflection across y-axis

  • f(x)=(-x)2

  • f(x)=2-x



Stretches and shrinks
Stretches and shrinks

  • If we multiply the function by a number GREATER THAN 1:

  • Vertical Stretch

  • f(x)=2x2

  • f(x)=3(2x)


Stretches and shrinks1
Stretches and shrinks

  • If we multiply the function by a number LESS THAN 1:

  • Vertical Shrink

  • f(x)=0.5x2

  • f(x)=0.2(2x)


Stretches and shrinks2
Stretches and shrinks

  • If we multiply the function by a number LESS THAN 1:

  • Vertical Shrink

  • f(x)=0.5x2

  • f(x)=0.2(2x)


Together
Together

How many transformations are there?

What are the transformations?

f(x)=x2-2


Together1
Together

How many transformations are there?

What are the transformations?

f(x)=x2-2

One transformation.

A vertical translation down 2


Together2
Together

How many transformations are there?

What are the transformations?

f(x)=2√x


Together3
Together

How many transformations are there?

What are the transformations?

f(x)=2√x

One transformation.

A vertical stretch by a factor of 2


Together4
Together

How many transformations are there?

What are the transformations?

f(x)=0.5(x-1)2


Together5
Together

How many transformations are there?

What are the transformations?

f(x)=0.5(x-1)2

Two transformations.

A vertical shrink by a factor of 0.5

Horizontal translation 1 right


Whiteboards
Whiteboards

  • Come up.

  • Take a Whiteboard.

  • And a transformations cheat-sheet.

  • No Black Friday recreations…


Whiteboards1
Whiteboards

  • Copy down the function into your notebook.

  • Solve it there.

  • Copy you answer to your board.


Round 1
Round 1

  • Identify the number of transformations.


Round 2
Round 2

  • Identify the TYPES of transformations.


Round 3
Round 3

  • Identify the transformations that have occurred to the parent function.



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