Unit 3: Relations and Functions Flashcards

Study Notes

Relations and Functions

A relation is defined as a set of ordered pairs representing the relationship between variables.
The independent variable, typically denoted as x, represents values chosen freely and influences the dependent variable.
The dependent variable, usually referred to as y, takes values that rely on the output of the independent variable.
A function is characterized by having precisely one output for each input, ensuring predictability in the relationship.
The domain encompasses all possible input values of a function, determining what x-values can be used.
The range includes all potential output values of a function, reflecting the resulting y-values.
Function notation provides a clear, systematic way to express a function, detailing inputs and corresponding outputs concisely.
A discrete function is represented graphically by isolated points, indicating distinct, non-continuous outputs.
In contrast, a continuous function displays a graph as an unbroken line or curve, indicating no interruptions in values.

Graph Characteristics

An x-intercept is the point where the graph crosses the x-axis, characterized by the y-coordinate being zero.
A y-intercept is where the graph crosses the y-axis, identified by the x-coordinate being zero.
Relative maximum points on a graph signify locations where neighboring points do not exceed the y-coordinate, indicating potential peaks.
Relative minimum points are those where no nearby points have a lesser y-coordinate, signifying valleys in the graph.

Symmetry and Function Types

Line symmetry refers to a situation where a line divides a figure into two halves that are mirror images, indicating symmetry in the graph.
A linear function is defined by a graph that forms a straight line, representing a constant rate of change between variables.

Description

Explore essential terms and definitions related to relations and functions in mathematics with these flashcards. Understand key concepts like independent and dependent variables, as well as the definition of a function.