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Function Translation Example

Function Translation Example
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2013-05-20 23:01
FunctionGraphing
This example demonstrates the transformation of the graph of f(x)=x^2 when shifted horizontally by k units, exploring the concept of function graph translation and the effect of variable transformation f(x+k). It utilizes GeoGebra commands like Point, Line, Sequence, If, Textfield, and TableText for construction. Suitable for high school students learning function graph transformations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → F
  2. Point(xAxis) → A
  3. Point(xAxis) → B
  4. Point(xAxis) → C
  5. Point(xAxis) → D
  6. Point(xAxis) → E
  7. Line((x(Corner[1]) + ((2 * indent) * screenwidth), 0), yAxis) → align1
  8. Line((x(Corner[1]) + ((3 * indent) * screenwidth), 0), yAxis) → align2
  9. Line((x(Corner[1]) + ((4 * indent) * screenwidth), 0), yAxis) → align3
  10. Sequence(p(Element[xValues, i]), i, 1, Length[xValues]) → pValues
  11. Sequence(f(Element[xValues, i]), i, 1, Length[xValues]) → fValues
  12. Sequence((Element[xValues, i], Element[fValues, i]), i, 1, Length[xValues]) → fPoints
  13. Sequence((Element[xValues, i], Element[pValues, i]), i, 1, Length[xValues]) → pPoints
  14. If(k ≥ 0, "+", "") → showsign
  15. If(k ≥ 0, "left", "right") → direction
  16. Textfield(f) → inputBox1
  17. TableText({{A1, B1, C1, D1, E1, F1}, {A2, B2, C2, D2, E2, F2}, {A3, B3, C3, D3, E3, F3}}, "|_") → tabletext

AI Drawing Prompt Reference

Create a visual example demonstrating the transformation of the graph of f(x)=x^2 when shifted horizontally by k units. Start by plotting several points on the x-axis, then draw three parallel lines through these points. Generate sequences for the values of f(x) and p(x+k), and connect these points to form the graphs. Include labels for the functions and the direction of translation beside the graph.
The prompt above was compiled from the original drawing commands and is for reference only.