function and relation. . ppt

function and relation

1. CHAPTER 1
UNDERSTANDING
FUNCTIONS
Lesson 1
Revisiting Functions
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2. 2
RELATIONSHIP

3. 3
Relation – a set of ordered pairs
(mother, child) (husband, wife) (God, man)
(employer, employee) (teacher, student)
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4. 4
Relation – a set of ordered pairs
{(mother, child)(husband, wife)(God, man)(employer, employee)(teacher, student)}husband,
Domain: The set of the first coordinates of the ordered pair.
God, employer, teacher
{
mother,
}
Range: The set of the second coordinates of the ordered pair.
{
Domain are x-values, inputs, independent variable.
Range are y-values, outputs, dependent variable.
child studentwife man employee
} , , , ,
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5. 5
There are many ways to represent relations:
These are all ways of
showing a
relationship between
two variables.
•A set of ordered pairs
•Mapping
•Table of values
•Graph
•Equation
y = x+1
Equation
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6. 6
TYPES OF RELATION
MAPPING
Philippines
Indonesia
Thailand
Manila
Jakarta
Bangkok
Domain Range
{(Philippines, Manila), (Indonesia, Jakarta), (Thailand, Bangkok)}
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7. 7
{(Mr. Mendoza, STEM A), (Mr. Mendoza, STEM B), (Mr. Mendoza, STEM C)}
Mr.
Mendoza
STEM A
STEM B
STEM C
Domain Range
MAPPING
TYPES OF RELATION
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8. MAPPING
{(Algebra, Mathematics), (Geometry, Mathematics), (Statistics,
Mathematics)}
Algebra
Geometry
Statistics
Mathematics
Domain Range
TYPES OF RELATION
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9. {(Statistics, STEM), (Statistics, ABM), (Statistics, TVL), (Calculus, STEM), (Gen Math,
STEM), (Gen Math, ABM), (Gen Math, TVL)}
Statistics STEM
ABM
TVL
Domain Range
Calculus
Gen Math
MAPPING
TYPES OF RELATION
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10. 10
TYPES OF RELATION
Philippines
Indonesia
Thailand
Manila
Jakarta
Bangkok
One to One
Domain Range
Mr.
Mendoza
STEM A
STEM B
STEM C
One to Many
Domain Range
Algebra
Geometry
Statistics
Mathematics
Many to One
Domain Range
SHS STEM
ABM
Tech Voc
Many to Many
Domain Range
Calculus
Gen Math
Statistics STEM
ABM
TVL
Many to Many
Domain Range
Calculus
Gen Math
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11. 11
Function
A function ( f ) is a correspondence between two sets, the
domain and the range, such that for each value in the domain,
there corresponds exactly one value in the range.
One to One
Many to One
One to Many
Many to Many
Is a RELATION a FUNCTION ?
If the set of ordered pairs have
different x-coordinates,
It is a FUNCTION!
If the set of ordered pairs have
same x-coordinates,
It is NOT a function
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12. 12
Practice Exercises
I. Determine if the following sets represent a function.
1. { ( 5, -1) , (4, -2) , (3, -3) , (2, -4) , (1, -5)}
Domain:
Range:
Function:
{5, 4, 3, 2, 1}
{-1, -2, -3, -4, -5}
YES!
2. { ( a, 1) , (b, 1) , (c, 1) , (d, 1) , (e, 1)}
Domain:
Range:
Function:
{a, b, c, d, e}
{1}
YES!
3. { (Manila, UST) , (Manila, Quiapo Church) , (Manila, Divisoria) , (Manila, Rizal Park)}
Domain:
Range:
Function:
{Manila}
{UST, Quiapo Church, Divisoria, Rizal Park}
NO!
One to One Type of Relation:
Type of Relation: Many to One
Type of Relation: One to Many
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13. 13
4.
x JanFebMarAprMay
y
3129313031
Domain:
Range:
Function:
5.
Math
Algebra
Geometry
Calculus
Statistics
Domain:
Range:
Function:
{Jan, Feb, Mar, Apr, May}
{31, 29, 30}
YES!
Domain:
Range:
Function:
{Algebra, Geomerty, Calculus, Statistics}
{Math}
NO!
Type of Relation: Many to One
Type of Relation: One to Many
6.
Domain:
Range:
Function:
Type of Relation:
{-4, -1, 0, 2, 4}
{-3, 3, -1, 2, 1}
YES!
One to One
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14. 14
VERTICAL LINE TEST
The set of points in the xy-plane is the graph of a function
if and only if every vertical line intersects the graph in
EXACTLY one point.
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15. If a vertical line passes through a graph more than once, the graph is not
the graph of a function.
NOT A
FUNCTION!
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16. FUNCTION!
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17. NOT A
FUNCTION!
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18. FUNCTION!
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19. NOT A
FUNCTION!
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20. NOT A
FUNCTION!
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Relation: 1-1 1-M M-1 M-M Relation: 1-1 1-M M-1 M-M

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Relation: 1-1 1-M M-1 M-M Relation: 1-1 1-M M-1 M-M

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Relation: 1-1 1-M M-1 M-M Relation: 1-1 1-M M-1 M-M

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Relation: 1-1 1-M M-1 M-M Relation: 1-1 1-M M-1 M-M

26. D: (-3, 3)
R: (-2, 4)
R: [-2, 4]
D: [-3, 3]
D: [-3, 3)
R: (-2, 4]
D: (-3, 3]
R: [-2, 4)
D: -3 ≤ x ≤ 3
R: -2 ≤ y ≤ 4
D: -3 ≤ x < 3
R: -2 < y ≤ 4
D: -3 < x ≤ 3
R: -2 ≤ y < 4
Domain and Range
Set Builder NotationInterval Notation
Interval NotationSet Builder Notation
Interval NotationSet Builder Notation
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