of 20
8/9/2019 2.1 Functions and Their Graphs (2)
1/20
2.1 Functions and
their Graphs
p. 67
8/9/2019 2.1 Functions and Their Graphs (2)
2/20
Assignment
Pp. 71-72 #5-48 a
8/9/2019 2.1 Functions and Their Graphs (2)
3/20
Relations
A relationis a mapping, or pairing, ofinput values with output values.
The set of input values is called the
domain. The set of output values is called therange.
A relation as a functionprovidedthere is exactly one output for eachinput.
It is NOTa function if at least oneinput has more than one output
8/9/2019 2.1 Functions and Their Graphs (2)
4/20
Input Output
-3 3
1 -2
4 1
4
Identify the Domain and Range. Thentell if the relation is a function.
Domain = !", #,$%Range = ",!&,#,$%
'unction()o* input # is mapped onto
+oth !& #
!otice the set notation"""
8/9/2019 2.1 Functions and Their Graphs (2)
5/20
denti$% the &omain and 'ange. (hen
te i$ the reation is a $unction.
Input Output
-3 3
1 1
3 -2
4
Domain = !", #,",$%
Range = ",#,!&%
'unction(-es* each input is mappedonto exactly one output
8/9/2019 2.1 Functions and Their Graphs (2)
6/20
A 'eation can )e represented )% a
set o$ orderedpairso$ the $orm *+,%
uadrant
/0, %0uadrant
/, %0
uadrant
/, %
uadrant 3/0, %
Origin (0,0)
8/9/2019 2.1 Functions and Their Graphs (2)
7/20
Graphing 'eations
(o graph the reation in the
preious e+ampe
rite as ordered pairs
*-,, *1,-2, *1,1, *4,4
Pot the points
8/9/2019 2.1 Functions and Their Graphs (2)
8/20
*-,*4,4
*1,1
*1,-2
8/9/2019 2.1 Functions and Their Graphs (2)
9/20
ame 9ith the points *-,,*1,1, *,1, *4,-2
8/9/2019 2.1 Functions and Their Graphs (2)
10/20
*-,
*4,-2
*1,1 *,1
8/9/2019 2.1 Functions and Their Graphs (2)
11/20
3ertica :ine (est
;ou can use the ertica ine test to isua%
determine i$ a reation is a $unction.
ide an% ertica ine *penci across the
graph to see i$ an% t9o points ie on the sameertica ine.
$ there are nott9o points on the same
ertica ine then the reation is a function.
$ there aret9o points on the same ertica
ine then the reation is NOT a function
8/9/2019 2.1 Functions and Their Graphs (2)
12/20
*-,*4,4
*1,1
*1,-2
Use the vertical line test to visually check if the
relation is a function.
Function?
No, To points are on
The sa!e vertical line.
8/9/2019 2.1 Functions and Their Graphs (2)
13/20
*-,
*4,-2
*1,1 *,1
Use the vertical line test to visually check if the
relation is a function.
Function?
"es, no to points are
on the sa!e vertical line
8/9/2019 2.1 Functions and Their Graphs (2)
14/20
Graphing and 2+-7
An ordered pairis a soution i$ the
e?uation is true 9hen the aues o$ + @ %are su)stituted into the e?uation.
2+-7 )ecause
- > 2*2 7 - > 4 7
- > -
8/9/2019 2.1 Functions and Their Graphs (2)
15/20
n an e?uation, the input varia$leis caedthe independent varia$le.
(he output varia$leis caed the
dependent varia$leand depends on theaue o$ the input aria)e.
n %>2+-7 B.. / is the independent ar.
; is the dependant ar. (he graph o$ an e?uation in 2 aria)es is
the coection o$ a points *+,% 9hose
coordinates are soutions o$ the e?uation.
8/9/2019 2.1 Functions and Their Graphs (2)
16/20
Graphing an e?uation in 2 aria)es
1. Construct a ta$le ofvalues
2. Graph enough soutionsto recogniDe a pattern
. Connect the points 9ith aine or cure
8/9/2019 2.1 Functions and Their Graphs (2)
17/20
%raph& y ' *
+tep *
Ta$le of values
+tep&+tep -&
8/9/2019 2.1 Functions and Their Graphs (2)
18/20
Function Notation E% naming the $unction $ %ou can 9rite
the function notation
f() ' ! $ Hthe aue o$ $ at +I
H$ o$ +I
$*+ is another name $or % *gro9n upname
;ou can use other etters $or $, iJe g or h
$ $
8/9/2019 2.1 Functions and Their Graphs (2)
19/20
&ecide i$ the $unction is inear. (hen
eauate $or + > -2
$*+ > -+2
+ K 5 !ot inearB.
$*-2 > -*-22 *-2 K 5
$*-2 > 7
g*+ > 2+ K 6
s inear )ecause + is to the $irst po9er
g*-2 > 2*-2 K 6 g*-2 > 2
(he domain $or )oth isB..
A reas
8/9/2019 2.1 Functions and Their Graphs (2)
20/20
