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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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