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Transformation of Functions

Transformation of Functions . Section 1.6. Objectives. Describe a transformed function given by an equation in words. Given a transformed common function, write the transformed function's equation. . Vocabulary. common function horizontal shift vertical shift vertical stretch/shrink

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Transformation of Functions

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  1. Transformation of Functions Section 1.6

  2. Objectives • Describe a transformed function given by an equation in words. • Given a transformed common function, write the transformed function's equation.

  3. Vocabulary • common function • horizontal shift • vertical shift • vertical stretch/shrink • reflect over the x-axis • reflect over the y-axis

  4. Common Functions

  5. Graph the functions and In general: Vertical shift up by c units

  6. Graph the functions and In general: Horizontal shift left by c units

  7. Graph the functions and In general: Vertical shift down by c units

  8. Graph the functions and In general: Horizontal shift right by c units

  9. Vertical shift up by c units Vertical shift down by c units Horizontal shift left by c units Horizontal shift right by c units Shift Summary • Vertical shifts • Horizontal shift

  10. Graph the functions and In general: Reflect over x-axis

  11. Graph the functions and In general: Reflect over y-axis

  12. Graph the functions and In general: Vertical stretch away from x-axis by a factor of c

  13. Graph the functions and In general: Vertical shrink toward x-axis by a factor of c

  14. Graph the functions and In general: Horizontal shrink toward y-axis by a factor of 1/c

  15. Graph the functions and In general: Horizontal stretch away from y-axis by a factor of 1/c

  16. Vertical stretch away from x-axis by a factor of c Vertical shrink toward x-axis by a factor of c Reflect over x-axis Stretch/Shrink/Reflection Summary • Vertical

  17. Horizontal stretch away from y-axis by a factor of 1/c Horizontal shrink toward y-axis by a factor of 1/c Reflect over y-axis Stretch/Shrink/Reflection Summary • Horizontal

  18. Given , after performing the following transformations:  shift to the left 76 units, shrink vertically by a factor of , and shift downward 13 units, write the new function.

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