Functions

Section 3.8

Multiple Choice

• A function is a correspondence between a first set, called the domain and a second set, called the range, such that each member of the domain corresponds to __________ member of the range.

• A. At least one

• B. Exactly one

• C. None of the above

Overview

• Functions and Graphs

• Function Notation and Equations

• Functions Defined Piecewise

• Linear Functions and Applications

Functions

• Function – Correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to exactly one member of the range

DOMAIN RANGECORRESPONDENCE

Example:To each person in class There corresponds A date of birth

To each bar code atHome Depot

There corresponds A price

To each real number There corresponds The cube of that number

Functions

DOMAIN:FoundingFathers

CORRESPONDENCE:

When that person signed the Declaration of Independence

John Hancock

Thomas McKean 1781

John Witherspoon

Thomas Jefferson

John Adams

Aug 2, 1776

RANGE:A set ofdates

Functions

DOMAIN:FoundingFathers

RANGE:

A set of dates

John Hancock

Thomas McKean June 24, 1817

John Witherspoon

Thomas Jefferson

John Adams

Oct 8, 1793

July 4, 1826

Nov 15, 1794

CORRESPONDENCE:

When they died

What is the Correspondence?

• Washington• Oregon• Idaho• Kansas• Montana• N. Dakota• Nebraska• Wyoming• Nevada

• Willow Goldfinch• Western Meadowlark• Mountain Bluebird

What is the Correspondence?

• Washington, My Home• Here We Have Idaho• Oregon, My Oregon• My Homeland Tennessee• When It’s Iris Time in

Tennessee• My Tennessee• The Tennessee Waltz• Rocky Top• Tennessee

• Washington• Idaho• Oregon• Tennessee

What is the Correspondence?

• 1• 2• 3• 4• 5

• 2• 3• 4• 5• 6

What is the Correspondence?

• 1• 2• 3• 4• 5

• 2• 4• 6• 8• 10

What is the Correspondence?

• 1• 2• 3• 4• 5

• 1• 4• 9• 16• 25

Functions and Graphs

• Functions can be expressed as ordered pairs• See graph on p 255

– Function is written as {(-3, 5), (1,2), (4,2)}– Domain is {-3, 1, 4}– Range is {5, 2}

• Functions generally represented by lower or upper case letters

• Abbreviation for real numbers• Closed dot indicates that point is on the graph• Open dot indicates point is not on graph

Functions and Graphs

• If graph has two or more points with same first coordinate, then NOT a graph of a function

• Vertical line test• Even if not a function, graph still represents

relations• Relation is a correspondence between domain

and range, such that each member of domain corresponds to a least one member of the range

Function Notations and Equations

• Element of domain is the input and the corresponding element of the range is output

• Function notation – f(x)– “f of x” or “f at x” or “the value of f at x”– x is the input and f(x) is the output– It does not mean f times x

• Often used in formulas

Functions Defined Piecewise

• Different equations for different parts of the domain

Linear Functions and Applications

• Linear function is any nonvertical line that passes vertical-line test and is the graph of a function

• f(x) = mx + b