đồng biến

Hàm số này đồng biến trên khoảng đã cho.

Definition

1. Adjective (Mathematics):
   • Monotonically increasing / Increasing: A function is described as "đồng biến" when its output value increases as its input value increases. For all x₁ and x₂ in the domain, if x₁ < x₂ then f(x₁) ≤ f(x₂). It is the property of being non-decreasing.
   • Directly proportional / Positively correlated: In a broader, non-technical sense, it can describe a relationship where two quantities change in the same direction; as one increases, the other also increases.

Usage Examples

• Adjective:
  • Hàm số y = 2x + 1 là hàm đồng biến trên R. (The function y = 2x + 1 is an increasing function over R.)
  • Có mối quan hệ đồng biến giữa nhiệt độ và áp suất. (There is a directly proportional relationship between temperature and pressure.)

Advanced Usage

• "Hàm số đồng biến": Increasing function.

  • Để tìm khoảng đồng biến, ta xét dấu của đạo hàm. (To find the interval of increase, we examine the sign of the derivative.)

• "Tính đồng biến": The property of being increasing / monotonic increase.

  • Tính đồng biến của hàm số được khảo sát kỹ. (The increasing nature of the function was thoroughly investigated.)

Variants and Related Words

• Nghịch biến (adj): Monotonically decreasing / decreasing. The opposite relationship.
  • Hàm số nghịch biến khi đạo hàm âm. (A function is decreasing when its derivative is negative.)

Synonyms

• Increasing: Going upward.
• Monotonic increase: Consistently non-decreasing.
• Positively correlated: Changing in the same direction.

Related Terms

• Đạo hàm (n): Derivative. Used to determine if a function is "đồng biến" (if the derivative is ≥ 0).
• Biến số (n): Variable.