Transformations

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