Solving Exponential Equations (I): Practice Generator with Graphical Check

Solving Exponential Equations (I): Practice Generator with Graphical Check
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2016-10-17 03:01
① This example demonstrates how to randomly generate exponential equation practice problems and verify solutions graphically by comparing function graphs, linking algebraic solving with visual confirmation. ② Core mathematical concepts include exponential equations, properties of exponential functions, the relationship between equation solutions and function zeros, and the use of random generation for exercise design. ③ Construction highlights: using GeoGebra commands Random, Sequence, Union, and RandomElement to generate random coefficients and bases, constructing exponential functions f and g, a button (button1) to trigger new problems, and text objects (text1 to text6) to display the problem and solution steps, while plotting the graphs for comparison. ④ Suitable for high school or pre-university students learning exponential equations, and useful for teachers as a classroom demonstration or for students' self-paced practice to grasp the geometric meaning of solutions.

GeoGebra Commands & Parameters

  1. Random(1, 3) → n
  2. Sequence(i, i, -10, -0.01, 0.01) → aseqleft
  3. Sequence(i, i, 0.01, 10, 0.01) → aseqright
  4. Union(aseqleft, aseqright) → aseq
  5. RandomElement(aseq) → a
  6. RandomElement(blist) → b
  7. Sequence(i, i, -0.999, -0.001, 0.001) → clistleft
  8. Sequence(i, i, 0.001, 0.999, 0.001) → clistright
  9. Union(clistleft, clistright) → clist
  10. RandomElement(clist) → c
  11. Sequence(i, i, 0.01, 10, 0.01) → tlist
  12. RandomElement(tlist) → t