1-Relations-and-Functions-Lecture.pdfhuij

Relations and Functions 1
Illustrating
Relations and
Functions

Essential Questions:
• What is a function?
• What are the characteristics of a function?
• How do you determine if a relation is a
function?
• How is a function different from a relation?
• Why is it important to know which variable is
the independent variable?
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Relation
◼ A relation between two variables x and y
is a set of ordered pairs
◼ An ordered pair consists of an x and y-
coordinate
◼ x-values are input, independent variable,
domain.
◼ y-values are output, dependent variable,
range
{( , ),( , ),( , ),( , ),( , ),( , )}
− − − − −
0 5 1 4 2 3 3 2 4 1 5 0

Example 1:
What makes this a relation?
{( , ),( , ),( , ),( , ),( , ),( , )}
− − − − −
0 5 1 4 2 3 3 2 4 1 5 0
•What is the domain?
{0, 1, 2, 3, 4, 5}
What is the range?
{-5, -4, -3, -2, -1, 0}

Example 2 –
Is this a relation?
•What is the domain?
{4, -5, 0, 9, -1}
•What is the range?
{-2, 7}
Input 4 –5 0 9 –1
–2 7
Output

Representation of Relation
Table of values Mapping Diagram Graph

Kinds of Relation

Relations and Functions
9
What is a function?
function
Mere relation

Is a relation a function?
•Focus on the x-coordinates, when given a relation
If the set of ordered pairs has different x-coordinates,
it IS A function
If the set of ordered pairs has same x-coordinates,
it is NOT a function
•Y-coordinates have no bearing in
determining functions

Example 3
{( , ),( , ),( , ),( , ),( , ),( , )}
− − − − −
0 5 1 4 2 3 3 2 4 1 5 0
•Is this a relation?
•Is this a function?
•Hint: Look only at the x-coordinates
YES
YES

Example 4
{(– , ),( , ),( , ),( , ),( , ),(– , )}
− − − −
1 7 1 0 2 3 0 8 0 5 2 1
•Is this a function?
•Hint: Look only at the x-coordinates
NO
•Is this still a relation?
YES

Relations and Functions
13
Choice One Choice Two
Example 5
3
1
0
–1
2
3
2
–1
3
2
3
–2
0
Which relation mapping represents a
function?
Choice 1

Example 6
Which relation mapping represents a function?
A. B.
B

5.

Piecewise Functions
◼ Some situations can only be
described by more than one
formula, depending on the
value of the independent
variable.

Problem 1
Give a function C that can
represent the cost of buying
x meals, if one meal costs
Php 40.00.
C(x) = 40x

Problem 2
A jeepney ride costs 8.00 Php for
the first 4 kilometers and each
additional integer kilometer
adds 1.50 Php to the fare. Use
a piecewise function to
represent the jeepney fare in
terms of the distance of d in
kilometers.

Problem 3
A man is charged 300Php monthly
for a particular mobile plan,
which includes 100 free text
messages. Messages in excess of
100 are charged 1 Php each.
Represent the amount a man
pays each month as a function
of the number of messages m
sent in a month.

Vertical Line Test
•Vertical Line Test: a relation is a function
if a vertical line drawn through its graph,
passes through only one point.
AKA: “The Pencil Test”
Take a pencil and move it from left to right
(–x to x); if it crosses more than one point,
it is not a function

Vertical Line Test
Would this
graph be a
function?
YES

Vertical Line Test
Would this
graph be a
function?
NO

1-Relations-and-Functions-Lecture.pdfhuij

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