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Transformations Mr. Markwalter

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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! - PowerPoint PPT Presentation

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Page 1: Transformations

TransformationsMr. Markwalter

Page 2: Transformations

Homecoming

Page 3: Transformations

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.

New Starting this Week…

Page 4: Transformations

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

So today we look at…

Before We Continue

Page 5: Transformations

Transformations!

Page 6: Transformations

Transformations change parent (simple) functions.

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

Transformations

Page 7: Transformations

What does absolute value do?

Transformations

Page 8: 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!

Transformations

Page 9: Transformations

f(x)+1

What Happened in #2

Page 10: Transformations

If we add a number outside of the original function:

VERTICAL TRANSLATION f(x)=x2+1 f(x)=2x-1

Translations!

Page 11: Transformations

If we add a number outside of the original function:

VERTICAL TRANSLATION (+ up, - down) f(x)=x2+1 f(x)=2x-1

Translations!

Page 12: Transformations

f(x+1)

What Happened in #3

Page 13: Transformations

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

Translations!

Page 14: Transformations

If we add a number INSIDE of the original function:

HORIZONTAL TRANSLATION (+ left, - right) f(x)=(x-1)2

f(x)=2x+1

Translations!

Page 15: Transformations

-f(x)

What Happened in #4

Page 16: Transformations

If we multiply by a negative OUTSIDE the original function:

VERTICAL Reflection across x-axis f(x)=-x2

f(x)=-2x

Reflections!

Page 17: Transformations

If we multiply by a negative OUTSIDE the original function:

VERTICAL Reflection across y-axis f(x)=-x2

f(x)=-2x

Reflections!

Page 18: Transformations

f(-x)

What Happened in #5

Page 19: Transformations

If we multiply the x by a negative: HORIZONTAL Reflection across y-axis f(x)=(-x)2

f(x)=2-x

Reflections!

Page 20: Transformations

If we multiply the x by a negative: HORIZONTAL Reflection across y-axis f(x)=(-x)2

f(x)=2-x

Reflections!

Page 21: Transformations

2f(x)

What Happened in #6

Page 22: Transformations

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

Vertical Stretch f(x)=2x2

f(x)=3(2x)

Stretches and shrinks

Page 23: Transformations

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

Vertical Shrink f(x)=0.5x2

f(x)=0.2(2x)

Stretches and shrinks

Page 24: Transformations

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

Vertical Shrink f(x)=0.5x2

f(x)=0.2(2x)

Stretches and shrinks

Page 25: Transformations

How many transformations are there?What are the transformations?

f(x)=x2-2

Together

Page 26: Transformations

How many transformations are there?What are the transformations?

f(x)=x2-2

One transformation.A vertical translation down 2

Together

Page 27: Transformations

How many transformations are there?What are the transformations?

f(x)=2√x

Together

Page 28: Transformations

How many transformations are there?What are the transformations?

f(x)=2√x

One transformation.A vertical stretch by a factor of 2

Together

Page 29: Transformations

How many transformations are there?What are the transformations?

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

Together

Page 30: Transformations

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 0.5Horizontal translation 1 right

Together

Page 31: Transformations

Come up. Take a Whiteboard. And a transformations cheat-sheet. No Black Friday recreations…

Whiteboards

Page 32: Transformations

Copy down the function into your notebook. Solve it there. Copy you answer to your board.

Whiteboards

Page 33: Transformations

Identify the number of transformations.

Round 1

Page 34: Transformations

Identify the TYPES of transformations.

Round 2

Page 35: Transformations

Identify the transformations that have occurred to the parent function.

Round 3

Page 36: Transformations

Get Started on the Worksheet