Transformations
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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


Homecoming

Homecoming


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…


Transformations1

Transformations!


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!


What happened in 2

What Happened in #2

  • f(x)+1


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


What happened in 3

What Happened in #3

  • f(x+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


What happened in 4

What Happened in #4

  • -f(x)


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


What happened in 5

What Happened in #5

  • f(-x)


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


What happened in 6

What Happened in #6

  • 2f(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.


Get started on the worksheet

Get Started on the Worksheet


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