Mr. Markwalter
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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.
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We need to make sure that we have the right
vocab to talk about our next topic.
So today we look at…
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Transformations change parent (simple)
functions.
Let’s take a look at the absolute value
function.
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What does absolute value do?
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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!
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f(x)+1
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If we add a number outside of the original
function:
VERTICAL TRANSLATION
f(x)=x2+1
f(x)=2x-1
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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
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f(x+1)
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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
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If we add a number INSIDE of the original
function:
HORIZONTAL TRANSLATION (+ left, - right)
f(x)=(x-1)2
f(x)=2x+1
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-f(x)
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If we multiply by a negative OUTSIDE the
original function:
VERTICAL Reflection across x-axis
f(x)=-x2
f(x)=-2x
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If we multiply by a negative OUTSIDE the
original function:
VERTICAL Reflection across y-axis
f(x)=-x2
f(x)=-2x
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f(-x)
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If we multiply the x by a negative:
HORIZONTAL Reflection across y-axis
f(x)=(-x)2
f(x)=2-x
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If we multiply the x by a negative:
HORIZONTAL Reflection across y-axis
f(x)=(-x)2
f(x)=2-x
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2f(x)
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If we multiply the function by a number
GREATER THAN 1:
Vertical Stretch
f(x)=2x2
f(x)=3(2x)
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If we multiply the function by a number LESS
THAN 1:
Vertical Shrink
f(x)=0.5x2
f(x)=0.2(2x)
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If we multiply the function by a number LESS
THAN 1:
Vertical Shrink
f(x)=0.5x2
f(x)=0.2(2x)
How many transformations are there?
What are the transformations?
f(x)=x2-2
How many transformations are there?
What are the transformations?
f(x)=x2-2
One transformation.
A vertical translation down 2
How many transformations are there?
What are the transformations?
f(x)=2√x
How many transformations are there?
What are the transformations?
f(x)=2√x
One transformation.
A vertical stretch by a factor of 2
How many transformations are there?
What are the transformations?
f(x)=0.5(x-1)2
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
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Come up.
Take a Whiteboard.
And a transformations cheat-sheet.
No Black Friday recreations…
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Copy down the function into your notebook.
Solve it there.
Copy you answer to your board.
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Identify the number of transformations.
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Identify the TYPES of transformations.
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Identify the transformations that have
occurred to the parent function.