mathematical function

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mathematical function

The teacher draws a graph of a mathematical function on the chalkboard.

Definition
  1. Noun:
    • A mathematical function is a precise rule or relationship that assigns exactly one output value from a set (called the range or codomain) to each input value from another set (called the domain). It describes how one quantity depends on or is determined by another.
Usage
  • The core concept is the unique association of one output for every input.
  • It is often represented by symbols like , where denotes the function and is an input from the domain.
  • Functions can be described using formulas, graphs, tables, or words.
Examples
  • Noun:
    • In the equation f(x) = 2x + 1, the mathematical function f doubles the input and then adds one.
    • The relationship between the side length of a square and its area is a mathematical function.
    • A graph showing temperature over time represents a mathematical function where time is the input and temperature is the output.
Advanced Usage
  • "To define a function": To formally specify the rule, domain, and range of a mathematical function.
    • We can define a function that maps each student to their test score.
  • "To evaluate a function": To compute the output of a function for a specific input.
    • To evaluate the function f(x) at x=3, substitute 3 for x in the formula.
  • "A function of": Used to express that one variable depends on another.
    • The distance traveled is a function of both speed and time.
Variants and Related Words
  • Function (n): The more general, abbreviated term for "mathematical function" in technical contexts.
    • The concept of a function is fundamental to calculus.
  • Mapping (n): A term often used synonymously with "function," emphasizing the idea of associating elements from one set to another.
    • The function describes a mapping from real numbers to real numbers.
  • Functional (adj): Pertaining to or having the nature of a function.
    • They studied the functional relationship between variables.
Synonyms
  • Mapping: (In mathematics) A correlation between sets where each element of the first set is associated with an element of the second set.
  • Transformation: Often used when the function implies a change or operation on the input.
Related Phrases
  • Domain of a function: The complete set of all possible input values for the function.
    • The domain of the function √x is all non-negative real numbers.
  • Range of a function: The complete set of all possible output values produced by the function.
    • The range of the function x² is all non-negative real numbers.
  • Continuous function: A function whose graph has no breaks, jumps, or holes.
  • Linear function: A function of the form , whose graph is a straight line.
mathematical function

The teacher draws a graph of a mathematical function on the chalkboard.

Noun
  1. (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)

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