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Understanding Geometric Transformations: Rotation, Translation, and Reflection

This guide explores essential geometric transformations such as rotation, translation, and reflection. We cover how these transformations manifest and their implications in mathematical functions. With hands-on examples using a graphing calculator (GDC), learn to identify the effects of horizontal and vertical translations on function graphs and how reflections affect their orientation. Understanding these concepts is crucial for deeper insights into functions and their graphical representations.

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Understanding Geometric Transformations: Rotation, Translation, and Reflection

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Presentation Transcript

  1. FUNCTIONS: TRANSFORMATIONS

  2. WHICH TRANSFORMATIONS DO YOU KNOW?

  3. WHICH TRANSFORMATIONS DO YOU KNOW? • ROTATION

  4. ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? • ROTATION

  5. ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? • ROTATION • TRANSLATION

  6. ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? • ROTATION • TRANSLATION • TRANSLATION

  7. ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? • ROTATION • TRANSLATION • REFLECTION • TRANSLATION

  8. ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? • ROTATION • TRANSLATION • REFLECTION • NOITCELFER • TRANSLATION

  9. ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? • ROTATION • TRANSLATION • REFLECTION • NOITCELFER • ENLARGEMENT • TRANSLATION

  10. ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? • ROTATION • TRANSLATION • REFLECTION • NOITCELFER • ENLARGEMENT • TRANSLATION • ENLARGEMENT

  11. What does this have To do with Functions??

  12. Withthe use of your GDC, graph:

  13. What do younotice???? Whattype of transformations do youhave ????

  14. Withthe use of your GDC, graph: TRANSLATIONS!!!!

  15. A HORIZONTAL translation takestheform: Series 1: Series 2:

  16. A VERTICAL translation takestheform: Series 1: Series 2:

  17. y = f ( x – a ): translation of f(x)alongthe x – axis of a unitstothe RIGHT. • y = f ( x + a ): translation of f(x)alongthe x – axis of a unitstothe LEFT. • y = f ( x ) + a: translation of f(x)alongthe y – axis of a units UP. • y = f ( x ) – a: translation of f(x)alongthe y – axis of a units DOWN.

  18. A REFLECTION aboutthe x - axis: Series 1: Series 2:

  19. A REFLECTION aboutthe x - axis: Series 1: Series 2:

  20. A REFLECTION aboutthe line y = x

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