tiwe0/geochat/exponential-log-transform

Claude Code and agent skill by tiwe0/geochat

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指数对数函数图像变换、定义域、单调性和交点比较的二级技能。

Install

npx vskill@latest install tiwe0/geochat/exponential-log-transform

SKILL.md

指数对数图像变换

适用于 y=a^x、y=log_a x 及其平移、伸缩、复合和比较大小问题。底数和定义域是第一约束。

工作顺序：

  1. 先写出底数限制、真数限制和定义域。
  2. 标出关键点、渐近线和单调方向。
  3. 比较大小时优先用单调性、同底化或图像交点。
  4. 参数题用滑块展示底数、平移量或交点个数变化。

关键规则：a^(x-h)+k 的水平渐近线是 y=k；log(a,x-h)+k 的定义域是 x>h、竖直渐近线是 x=h；写成 x-h 表示向右平移 h，不要把符号读反。

原生输入小例子

在空白构图中逐行输入；名称冲突时改名，不覆盖用户对象。

ggb
expShiftELT(x) = 2^(x - 1) + 3
logShiftELT(x) = log(2, x - 1) + 3
horizontalAsymptoteELT: y = 3
verticalAsymptoteELT: x = 1
ExpKeyELT = (1, expShiftELT(1))
LogKeyELT = (2, logShiftELT(2))
logBoundaryELT = logShiftELT(1)

预期：ExpKeyELT=(1,4)、LogKeyELT=(2,3)、logBoundaryELT 未定义；指数图像趋近 y=3 但不相交，对数图像只在 x>1 定义。正常验证检查关键点；边界验证代入 x=1；退化验证平移量为 0 时渐近线恢复坐标轴，而底数为 1 时对数模型非法。

官方参考：预定义函数与运算符、Asymptote。

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