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Demonstration of Slopes in Function Composition

Demonstration of Slopes in Function Composition
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2015-06-18 06:15
FunctionCoordinate GeometryDerivativeSlider AnimationGraphing
This example illustrates the relationship between the slopes of composite linear functions. Key math concepts include function composition, linear function slopes, and the product rule for slopes. GeoGebra commands used are Expand, TableText, Point, Line, and Slope, along with objects like m, n, b, c, f, g, h, gof, text1, A, B, a, C, D, d, E, F, e, m_1, m_2, m_3. It is suitable for high school mathematics instruction on understanding function composition and slope calculations.

GeoGebra Commands & Parameters

  1. Expand(h) → gof
  2. TableText({{LaTeX[f, true, true]}, {LaTeX[g, true, true]}, {LaTeX[gof, true, true]}}) → text1
  3. Point(gof) → A
  4. Point(gof) → B
  5. Line(A, B) → a
  6. Point(f) → C
  7. Point(f) → D
  8. Line(C, D) → d
  9. Point(g) → E
  10. Point(g) → F
  11. Line(E, F) → e
  12. Slope(a) → m_1
  13. Slope(d) → m_2
  14. Slope(e) → m_3

AI Drawing Prompt Reference

Draw two linear functions f and g, and their composition gof. First, plot f and g, then plot gof. Calculate and display the slopes m1, m2, and m3 of f, g, and gof respectively.
The prompt above was compiled from the original drawing commands and is for reference only.