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THE SQUARE ROOT FUNCTION
Section 3.4
Library of Functions;
Piecewise-Defined Functions
Propertiesof
1. Thedomainandrangeareboththeset
ofnonnegativerealnumbers;thatis,
0, ∞ .
2. The ‐interceptofthegraphis 0, 0 .
The ‐interceptofthegraphisalso
0, 0 .
3. Thefunctionisneitherevennorodd.
4. Itisincreasingontheinterval 0, ∞ .
5. Ithasalocalminimumof0at
0.
THE ABSOLUTE VALUE
FUNCTION
THE CUBE ROOT FUNCTION
Propertiesof
1. Thedomainandrangearethesetofall
realnumbers;thatis, ∞, ∞ .
2. The ‐interceptis 0, 0 .The ‐
interceptisalso 0, 0 .
3. Thefunctionisodd.
4. Itisincreasingontheinterval ∞, ∞ .
5. Itdoesnothavealocalminimumora
localmaximum.
Propertiesof
1. Thedomainisthesetofallrealnumbers;
thatis, ∞, ∞ .Therangeisall
nonnegativerealnumbers;thatis, 0, ∞ .
2. The ‐interceptofthegraphis 0, 0 .The
‐interceptofthegraphisalso 0, 0 .
LIBRARY OF FUNCTIONS
LIBRARY (CONTINUED)
3. Thefunctioniseven.
4. Itisdecreasingontheinterval ∞, 0 .It
isincreasingontheinterval 0, ∞ .
5. Ithasalocalminimumof0at
0.
1. ConstantFunction:
Domain: ∞, ∞
Itsgraphisahorizontalline.
Its ‐interceptis 0, .
Itisconstantontheentiredomain.
3. LinearFunction:
Domain: ∞, ∞
Itsgraphisaline.
Its ‐interceptis 0, .
Increasingif
0.Decreasingif
0.
Itistheconstantfunctionif
0.
Itistheidentityfunctionif
1 and
0.
2.
4.
IdentityFunction:
Domain: ∞, ∞
Itsgraphisaline.
Itsy‐interceptis 0, 0 .
Itisincreasingontheentiredomain.
SquareFunction:
Domain: ∞, ∞
Itsgraphisaparabola.
Itsy‐interceptis 0, 0 .
Itisdecreasingon ∞, 0 andincreasingon 0, ∞).
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LIBRARY (CONTINUED)
5.
LIBRARY (CONTINUED)
7.
CubeFunction:
Domain: ∞, ∞
Its ‐interceptis 0, 0 .
Itisincreasingon ∞, ∞ .
8.
6.
9.
SquareRootFunction:
Domain: 0, ∞
Itsgraphisahalfparabola.
Its ‐interceptis 0, 0 .
Itisincreasingontheinterval 0, ∞ .
CubeRootFunction:
Domain: ∞, ∞
Its ‐interceptis 0, 0 .
Itisincreasing.
ReciprocalFunction:
Domain: ∞, 0 ∪ 0, ∞
Ithasnointercepts.
Itisdecreasingontheintervals
∞, 0 and 0, ∞ .
LIBRARY (CONTINUED)
PIECEWISE-DEFINED
FUNCTIONS
AbsoluteValueFunction:
Domain: ∞, ∞ Its ‐interceptis 0, 0 .
Itisdecreasingontheinterval ∞, 0 and
increasingontheinterval 0, ∞ .
Apiecewise‐definedfunction isafunction
thatisdefinedbymorethanoneequation.An
exampleis
10. GreatestIntegerFunction:
Domain: ∞, ∞
Itisanexampleofastepfunction.
Its ‐interceptis 0, 0 .
Itisconstantontheintervals ,
isanyinteger.
int
1
2
if
if
1
if
1
1
1
1 where
2