Understanding Functions and Graphs in Mathematics
Functions are a fundamental concept in mathematics used to describe relationships in the real world. They can be represented through equations, graphs, tables, or verbal descriptions. A function maps elements from a domain to a range, where each input has a unique output. The domain encompasses all possible input values, while the range comprises the corresponding output values. Graphs visually represent functions in the Cartesian plane, showing the relationship between input and output pairs.
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Mathematics General concepts
1.1 Functions and Their Graphs Functions are a tool for describing the real world in mathematical terms. A function can be represented by an equation, a graph, a numerical table, or a verbal description. This section reviews these function ideas.
Function DEFINITION A function from a set D to a set Y is a rule that assigns a unique (single) element (x) Y to each element x D. The set D of all possible input values is called the domain of the function. The set of all output values of (x) as x varies throughout D is called the range of the function. The range may not include every element in the set Y. The domain and range of a function can be any sets of objects, but often in calculus they are sets of real numbers interpreted as points of a coordinate line.
Graphs of Functions If is a function with domain D, its graph consists of the points in the Cartesian plane whose coordinates are the input-output pairs for .
