Relations and Functions Overview

Study Notes

Key Concepts in Relations and Functions

Relation: Consists of ordered pairs, establishing a connection between elements from two sets.
Mapping: Visual representation showing how each domain element corresponds to a range element.

Domain and Range

Domain: The complete set of x-coordinates or inputs in a relation that can be taken into account.
Range: The complete set of y-coordinates or outputs resulting from the relation.

Variables in Relations

Independent Variable: Typically represented as x; its value is chosen freely, influencing the dependent variable.
Dependent Variable: Typically represented as y; its value changes in response to the independent variable.

Functions

Function: A specialized type of relation where each input (domain) corresponds to a unique output (range).
Discrete Function: Comprised of distinct, individual points; not continuous.
Continuous Functions: Graphable as a single line or smooth curve, indicating unbroken data.

Graphical Analysis

Vertical Line Test: A method to check if a graph represents a function; it must not intersect the graph more than once.

Functional Representation

Function Notation: A systematic way to denote a function, typically using an equation format.
Variable: A symbol (often a letter) that signifies a number within mathematical expressions.
Algebraic Expression: Combination of numbers, variables, and operational symbols illustrating mathematical relationships.

Description

This quiz covers key concepts related to relations and functions, including definitions of domain, range, independent and dependent variables. Explore the distinctions between different types of functions and their representations in mathematics.