乘除运算对不等式的影响
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①本范例演示乘除运算对两量间不等式关系的影响;②涉及核心数学概念:不等式性质、乘除运算规则;③作图要点:运用了Function, Point, If, Textfield, Sequence, CircumcircleArc, RandomElement, Random, Sum等GeoGebra命令与对象;④适合初中及以上学生,用于理解不等式在乘除运算下的变化规律。
GeoGebra 命令及参数
Function(ticksize / 4, lowerbound - 0.5, upperbound + 0.5) → abovenumlinePoint(abovenumline) → A_dIf(p_{boolean} ≟ true, Random[lowerbound + 5, upperbound - 5], x(A_d)) → x_ATextfield(ticksize) → inputBox3Textfield(lowerbound) → inputBox1Textfield(upperbound) → inputBox2Function(0, lowerbound - 0.5, upperbound + 0.5) → numlineSequence((i, 0), i, lowerbound, upperbound, 1) → listTicksSequence(Text[i, (i - ticksize / 5, -0.95)], i, lowerbound, upperbound, ticksize) → ListxaxisNumbersPoint(abovenumline) → B_dIf(p_{boolean} ≟ true, Random[lowerbound + 5, upperbound - 5], x(B_d)) → x_BTextfield(k) → inputBox4If(SelectedIndex[ListOperation] > 2, 1 / k^(2), 1) → reciprolkCircumcircleArc(A, M_{A'A}, A') → cCircumcircleArc(B, M_{B'B}, B') → dTextfield(k) → InputBoxFactorIf(k > 0, "No", "Yes") → InequalityChangeIf(SelectedElement[ListUserAnswerInequalityChange] ≟ InequalityChange, true, false) → CorrectAnswertoInequalityIf(x(A) > x(B), 3, 2) → Num1GreaterRandomElement({-3, 2, -1, 3, -2, 2}) → kRandomIf(x(A') > x(B'), 3, 2) → Num1newGreaterRandom(2, 3) → OpNumRandomIf(x(A) < 0, floor(lg(abs(x(A)))) + 3, If[x(A) ≟ 0, 1, floor(lg(abs(x(A)))) + 1]) → n_{Aspace}If(x(B) < 0, floor(lg(abs(x(B)))) + 2, floor(lg(abs(x(B)))) + 1) → n_{Bspace}Sum(Sequence[{"\;"}, i, 1, 5 - n_{Aspace}]) → listspaceAIf(SelectedIndex[listInput10thLine1] ≟ 2 ∧ k > 0 ∨ SelectedIndex[listInput10thLine1] ≟ 3 ∧ k < 0, true, false) → correctconclusion