MathPlotAI Logo MathPlotAI

Graph Transformations Review

Graph Transformations Review
Loading the math board and drawing, please wait…
2014-11-16 02:42
FunctionTransformationGraphing
This GeoGebra applet is designed to demonstrate basic graph transformations. It is suitable for precalculus and calculus classes, helping students understand transformations such as translations, stretches, and symmetries of function graphs. The applet uses slider animations, loci, and graphing commands in GeoGebra. Suitable for high school and university beginners.

GeoGebra Commands & Parameters

  1. Numeric Step(10.0)
  2. Numeric a(1.0)
  3. f(x) = x^(3) + a
  4. Numeric b(0.0)
  5. g(x) = (x + b)^(2)
  6. Numeric c(1.0)
  7. h(x) = ((c * x))^(1 / 2)
  8. Numeric d(1.0)
  9. htwo(x) = ((d * x))^(1 / 2)
  10. ione(x) = x^(2) - (2 * x) + 1
  11. itwo(x) = (-ione(x))
  12. Boolean e(false)
  13. red(x) = (-((x - 3)^(2) + (2 * (x - 3)) - 3 + 1))
  14. Numeric l(1.0)
  15. Numeric m(1.0)
  16. Numeric n(0.0)
  17. blue(x) = (l * ((x - m)^(2) + (2 * (x - m)) - 3 + n))

AI Drawing Prompt Reference

Draw a graph showing function transformations with several curves in one coordinate system. Include a cubic curve that shifts vertically with a slider, a parabola that shifts horizontally, and two square-root curves with different vertical stretches. Also show a quadratic curve and its reflection across the x-axis, plus a transformed blue curve obtained by shifting and scaling the original quadratic. Use sliders to adjust parameters for translations, stretches, and symmetry, making the effects of each transformation visible.
The prompt above was compiled from the original drawing commands and is for reference only.