Relations and Functions Overview

Questions and Answers

What is a relation?

A number

A set of ordered pairs (correct)

An equation

An operation

What does mapping illustrate in a relation?

How each element of the domain is paired with an element in the range

What is the range in a relation?

The set of y-coordinates

What is the domain in a relation?

The set of x-coordinates Signup and view all the answers

What is the independent variable in a relation?

The variable with a value that is subject to choice, usually x Signup and view all the answers

What is the dependent variable in a relation?

The variable that depends on the value of the independent variable, usually y Signup and view all the answers

What defines a function?

A relation where each domain element is paired with exactly one range element Signup and view all the answers

What is a discrete function?

A function of points that are not connected Signup and view all the answers

What are continuous functions?

Functions that can be graphed with a line or a smooth curve Signup and view all the answers

What is the vertical line test used for?

To determine if a graph is a function Signup and view all the answers

What is function notation?

A way to name a function defined by an equation Signup and view all the answers

What is a variable in algebra?

A letter that represents a number Signup and view all the answers

What is an algebraic expression?

One or more numbers and variables with operations Signup and view all the answers

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.