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関数の分類.mermaid

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Jul 27th, 2026
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  1. graph TD
  2. %% ノード
  3. Root["関数の分類"]
  4.  
  5. Change["値の変化"]
  6. Equation["式の形"]
  7.  
  8. Nondecreasing["非減少<br>x₁ ≤ x₂ ⟹ f(x₁) ≤ f(x₂)"]
  9. Nonincreasing["非増加<br>x₁ ≤ x₂ ⟹ f(x₁) ≥ f(x₂)"]
  10.  
  11. Increasing["増加<br>x₁ < x₂ ⟹ f(x₁) < f(x₂)"]
  12. Decreasing["減少<br>x₁ < x₂ ⟹ f(x₁) > f(x₂)"]
  13.  
  14. Rational["有理関数"]
  15.  
  16. Polynomial["多項式関数"]
  17. Fractional["分数関数"]
  18.  
  19. Affine["アフィン関数<br>y = ax + b"]
  20.  
  21. Constant["定数関数<br>y = b"]
  22. Linear["線形関数<br>y = ax"]
  23. DegreeOne["1次関数<br>y = ax + b (a ≠ 0)"]
  24.  
  25. Zero["零関数<br>y = 0"]
  26. Direct["比例<br>y = ax (a ≠ 0)"]
  27.  
  28. Inverse["反比例<br>y = a⋅1/x (a ≠ 0)"]
  29.  
  30. %% エッジ(包含関係)
  31. Root --> Change
  32. Root --> Equation
  33.  
  34. Change --> Nondecreasing
  35. Change --> Nonincreasing
  36.  
  37. Nondecreasing --> Increasing
  38. Nonincreasing --> Decreasing
  39.  
  40. Equation --> Rational
  41.  
  42. Rational --> Polynomial
  43. Rational --> Fractional
  44.  
  45. Polynomial --> Affine
  46.  
  47. Affine -->|a = 0| Constant
  48. Affine -->|b = 0| Linear
  49. Affine -->|a ≠ 0| DegreeOne
  50.  
  51. Constant -->|b = 0| Zero
  52. Linear -->|a = 0| Zero
  53. Linear -->|a ≠ 0| Direct
  54. DegreeOne -->|b = 0| Direct
  55.  
  56. Fractional --> Inverse
  57.  
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