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Section 3.5 – Transformation of Functions

Section 3.5 – Transformation of Functions. Symmetry. Symmetric with respect to an axis : You can fold a graph along an axis and the graph will fall on top of itself. Each part of the graph is covered by its image.

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Section 3.5 – Transformation of Functions

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  1. Section 3.5 – Transformation of Functions

  2. Symmetry Symmetric with respect to an axis: You can fold a graph along an axis and the graph will fall on top of itself. Each part of the graph is covered by its image. Symmetric with respect to the origin: Rotating a graph 180⁰ about the origin results in the original graph. You can also fold along the x-axis AND the y-axis and the graph will fall on top of itself.

  3. Symmetric with respect to axis If the graph is symmetric with respect to the x-axis, the x-value stays the same!

  4. Symmetric with respect to axis If the graph is symmetric with respect to the y-axis, the y-value stays the same!

  5. Symmetric With Respect to the Origin If the graph is symmetric with respect to the origin, NOTHING stays the same!

  6. Even and Odd Functions Functions CAN’T be BOTH even and odd! They may be neither!

  7. Even and Odd Functions Determine whether the function is even, odd, or neither even nor odd. NOT EVEN NOT ODD NEITHER

  8. Even and Odd Functions Determine whether the function is even, odd, or neither even nor odd. NOT EVEN ODD

  9. Horizontal Translations

  10. Horizontal Translations

  11. Horizontal Translations

  12. Horizontal Translations

  13. VERTICALTranslations

  14. VERTICALTranslations

  15. VERTICALTranslations

  16. REFLECTIONS ACROSS THE AXIS

  17. REFLECTIONS ACROSS THE AXIS

  18. REFLECTIONS ACROSS THE AXIS

  19. VERTICAL STRETCHING OR SHRINKING

  20. VERTICAL STRETCHING OR SHRINKING

  21. VERTICAL STRETCHING OR SHRINKING

  22. Transformations Describe the transformations associated with the function and then graph the function. Basic Function: Shift 1 unit to the left Shift down 5 units

  23. Transformations Describe the transformations associated with the function and then graph the function. Basic Function: Shift 4 units to the right Reflect over axis Shift up 1 unit

  24. Transformations

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