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### Transformations

Mr. Markwalter

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

- We need to make sure that we have the right vocab to talk about our next topic.
- So today we look at…

Transformations

- Transformations change parent (simple) functions.
- Let’s take a look at the absolute value function.

Transformations

- What does absolute value do?

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

- f(x)+1

Translations!

- If we add a number outside of the original function:
- VERTICAL TRANSLATION
- f(x)=x2+1
- f(x)=2x-1

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

- f(x+1)

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

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

- -f(x)

Reflections!

- If we multiply by a negative OUTSIDE the original function:
- VERTICAL Reflection across x-axis
- f(x)=-x2
- f(x)=-2x

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

- f(-x)

Reflections!

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

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

- 2f(x)

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 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 shrinks

- If we multiply the function by a number LESS THAN 1:
- Vertical Shrink
- f(x)=0.5x2
- f(x)=0.2(2x)

Together

How many transformations are there?

What are the transformations?

f(x)=x2-2

One transformation.

A vertical translation down 2

Together

How many transformations are there?

What are the transformations?

f(x)=2√x

One transformation.

A vertical stretch by a factor of 2

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

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

Whiteboards

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

Round 1

- Identify the number of transformations.

Round 2

- Identify the TYPES of transformations.

Round 3

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

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