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Transformations

Get ready for homecoming as Mr. Markwalter introduces quizzes on transformations every Friday. Discover the impact of vertical and horizontal translations, reflections, and stretches/shrinks on functions in this engaging lesson. Come prepared with your notes and be ready to identify various transformations to boost your grades. Practice on whiteboards and worksheets to master these concepts easily!

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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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