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Transformations

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

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  1. Transformations Mr. Markwalter

  2. Homecoming

  3. 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.

  4. 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…

  5. Transformations!

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

  7. Transformations • What does absolute value do?

  8. 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!

  9. What Happened in #2 • f(x)+1

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

  11. Translations! • If we add a number outside of the original function: • VERTICAL TRANSLATION (+ up, - down) • f(x)=x2+1 • f(x)=2x-1

  12. What Happened in #3 • f(x+1)

  13. 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

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

  15. What Happened in #4 • -f(x)

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

  17. Reflections! • If we multiply by a negative OUTSIDE the original function: • VERTICAL Reflection across y-axis • f(x)=-x2 • f(x)=-2x

  18. What Happened in #5 • f(-x)

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

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

  21. What Happened in #6 • 2f(x)

  22. Stretches and shrinks • If we multiply the function by a number GREATER THAN 1: • Vertical Stretch • f(x)=2x2 • f(x)=3(2x)

  23. 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)

  24. 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)

  25. Together How many transformations are there? What are the transformations? f(x)=x2-2

  26. Together How many transformations are there? What are the transformations? f(x)=x2-2 One transformation. A vertical translation down 2

  27. Together How many transformations are there? What are the transformations? f(x)=2√x

  28. Together How many transformations are there? What are the transformations? f(x)=2√x One transformation. A vertical stretch by a factor of 2

  29. Together How many transformations are there? What are the transformations? f(x)=0.5(x-1)2

  30. 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

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

  32. Whiteboards • Copy down the function into your notebook. • Solve it there. • Copy you answer to your board.

  33. Round 1 • Identify the number of transformations.

  34. Round 2 • Identify the TYPES of transformations.

  35. Round 3 • Identify the transformations that have occurred to the parent function.

  36. Get Started on the Worksheet

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