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Function Reflections Rule Exploration

Function Reflections Rule Exploration
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2012-09-03 04:09
FunctionCoordinate GeometryTransformationGraphing
In collections Function transformation, translations, and reflections
This GeoGebra example guides students in discovering the rules for reflecting functions across the x-axis, y-axis, and origin. Through interactive manipulation, learners explore function reflections, symmetry, and geometric transformations. Construction uses PolyLine and Mirror commands along with point sets A–E and their image objects. Ideal for high school function units, it supports visual understanding of function transformations and symmetry in coordinate geometry.

GeoGebra Commands & Parameters

  1. PolyLine(A, B, C, D, E) → a
  2. Mirror(A, xAxis) → A'
  3. Mirror(B, xAxis) → B'
  4. Mirror(C, xAxis) → C'
  5. Mirror(D, xAxis) → D'
  6. Mirror(E, xAxis) → E'
  7. PolyLine(A', B', C', D', E') → a'
  8. Mirror(A, yAxis) → A'_1
  9. Mirror(B, yAxis) → B'_1
  10. Mirror(C, yAxis) → C'_1
  11. Mirror(D, yAxis) → D'_1
  12. Mirror(E, yAxis) → E'_1
  13. PolyLine(A'_1, B'_1, C'_1, D'_1, E'_1) → a'_1
  14. Mirror(A', yAxis) → A''
  15. Mirror(B', yAxis) → B''
  16. Mirror(C', yAxis) → C''
  17. Mirror(D', yAxis) → D''
  18. Mirror(E', yAxis) → E''
  19. PolyLine(A'', B'', C'', D'', E'') → a''