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Horizontal Transformations Exploration

Horizontal Transformations Exploration
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2020-11-17 15:20
FunctionCalculusTransformationGraphing
In collections Grade 12 PreCalculus BC
This example demonstrates the effects of horizontal transformations on function graphs by dynamically adjusting parameters b and c to observe shifts in the graph. Key math concepts include function transformations, geometric interpretations, and parameter influence. GeoGebra commands and objects used in construction are highlighted, such as If, Text, Slider, and objects like d, a, b, c, gright, gleft. It is suitable for high school mathematics education to enhance understanding of function transformation properties and integrate visual intuition with abstract thinking.

GeoGebra Commands & Parameters

  1. If(b < 0, 4 / ((-b)) + c, 4 / b + c) → gright
  2. If(b < 0, 4 / b + c, -4 / b + c) → gleft
  3. Text(abs(c)) → absctext
  4. If(b ≟ 1, "", If[b ≟ -1, "-", Text[b]]) → btext
  5. If(c ≟ 0, gtext0, If[c < 0, gtextpc, gtextmc]) → gtext
  6. If(c ≟ 0, ftextc0, If[c < 0, ftextpc, ftextmc]) → ftext
  7. If(b < 0, -8 / ((-b)) + c, -2 / b + c) → fleft
  8. If(b < 0, 2 / ((-b)) + c, 8 / b + c) → fright

AI Drawing Prompt Reference

Create a diagram exploring horizontal transformations of function graphs using adjustable parameters b and c, showing how c shifts graphs horizontally and how b’s sign and special values (1, −1, and 0) affect the left/right forms. Plot a right curve labeled gright defined piecewise: if b<0 use 4/(-b)+c, otherwise use 4/b+c. Plot a left curve labeled gleft: if b<0 use 4/b+c, otherwise use −4/b+c. Add corresponding text annotations: display abs(c) as absctext, show the appropriate symbol/value for b as btext, and render sign-based labels for c as gtext and ftext depending on whether c equals 0 or is negative. Finally, add two more piecewise curves fleft and fright: for fleft use −8/(-b)+c when b<0, otherwise −2/b+c; for fright use 2/(-b)+c when b<0, otherwise 8/b+c. Arrange the left and right curves together with their textual labels to visualize horizontal shift and direction changes.
The prompt above was compiled from the original drawing commands and is for reference only.