Mr. Markwalter.  I have noticed that some people are really only choosing to study seriously when a test comes close.  We are going to start quizzes.

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Presentation transcript:

Mr. Markwalter

 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.

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

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

 What does absolute value do?

 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!

 f(x)+1

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

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

 f(x+1)

 If we add a number INSIDE of the original function:  HORIZONTAL TRANSLATION (positive left, negative right)  f(x)=(x-1) 2  f(x)=2 x+1

 If we add a number INSIDE of the original function:  HORIZONTAL TRANSLATION (+ left, - right)  f(x)=(x-1) 2  f(x)=2 x+1

 -f(x)

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

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

 f(-x)

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

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

 2f(x)

 If we multiply the function by a number GREATER THAN 1:  Vertical Stretch  f(x)=2x 2  f(x)=3(2 x )

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

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

How many transformations are there? What are the transformations? f(x)=x 2 -2

How many transformations are there? What are the transformations? f(x)=x 2 -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

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

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

 Identify the number of transformations.

 Identify the TYPES of transformations.

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