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! - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/1.jpg)
TransformationsMr. Markwalter
![Page 2: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/2.jpg)
Homecoming
![Page 3: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/3.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/4.jpg)
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
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Transformations!
![Page 6: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/6.jpg)
Transformations change parent (simple) functions.
Let’s take a look at the absolute value function.
Transformations
![Page 7: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/7.jpg)
What does absolute value do?
Transformations
![Page 8: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/8.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/9.jpg)
f(x)+1
What Happened in #2
![Page 10: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/10.jpg)
If we add a number outside of the original function:
VERTICAL TRANSLATION f(x)=x2+1 f(x)=2x-1
Translations!
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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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/12.jpg)
f(x+1)
What Happened in #3
![Page 13: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/13.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/14.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/15.jpg)
-f(x)
What Happened in #4
![Page 16: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/16.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/17.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/18.jpg)
f(-x)
What Happened in #5
![Page 19: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/19.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/20.jpg)
If we multiply the x by a negative: HORIZONTAL Reflection across y-axis f(x)=(-x)2
f(x)=2-x
Reflections!
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2f(x)
What Happened in #6
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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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/23.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/24.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/25.jpg)
How many transformations are there?What are the transformations?
f(x)=x2-2
Together
![Page 26: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/26.jpg)
How many transformations are there?What are the transformations?
f(x)=x2-2
One transformation.A vertical translation down 2
Together
![Page 27: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/27.jpg)
How many transformations are there?What are the transformations?
f(x)=2√x
Together
![Page 28: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/28.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/29.jpg)
How many transformations are there?What are the transformations?
f(x)=0.5(x-1)2
Together
![Page 30: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/30.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/31.jpg)
Come up. Take a Whiteboard. And a transformations cheat-sheet. No Black Friday recreations…
Whiteboards
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Copy down the function into your notebook. Solve it there. Copy you answer to your board.
Whiteboards
![Page 33: Transformations](https://reader035.vdocuments.site/reader035/viewer/2022070421/568161a6550346895dd1646f/html5/thumbnails/33.jpg)
Identify the number of transformations.
Round 1
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Identify the TYPES of transformations.
Round 2
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Identify the transformations that have occurred to the parent function.
Round 3
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Get Started on the Worksheet