Transcript 1.2 Relations and Functions

1.2 Relations and Functions
Quiz:
Fill in the blank of the following sentences:
A relation is a set if ____ pairs.
Real Number System
Natural Number(whole number)
1, 2, 3, 4, …,100,…1000,…1242345
Integer
…, -5, -3, -1, 0, 1, 2, 3, 4, 5,…
Rational Number
m/n, such as 1, 3, 1/3, 0.33333,…
Real Number
numbers that can be written as decimal numbers
Real Number System
Real Numbers
Rational
Numbers
Integers
Natural
Numbers
Set-Builder Notation and Interval
Notation
Set-Builder Notation
Form: {variable | inequalities}
example: {x|x>2}, {y|-5<y≤4}, {u|u<0}
Interval Notation( and corresponding graph)
Form: (a,b), [a,b], (a,b], [a,b)
example: (1,5), [0.5, 7.2], [2, ∞), (- ∞, 0]
Set-Builder Notation and Interval
Notation
Excersices
1, any real number that is greater than 5.
2, any real number that is between -2 and 2 and equal to -2 and
2.
3, all real numbers except 0.
4, all real numbers.
Relation, Domain and Range
Relation: a set of ordered pairs.
{(a1,b1),(a2,b2),(a3,b3)…}
(x , y)
Domain
Range
Relations, Domain, and Range
Examples:
F={(1,2),(2,5),(3,7)}
G={(-1,0),(0,2),(1,4),(2,6)}
H={(-2,0),(-2,1),(-1,0),(0,1)}
Relations, Domain, and Range
How to illustrate a relation by a table
F= {(-3,2),(-1,3),(2,1)}
Domain
Range
Relations, Domain, and Range
How to illustrate a relation with a graph
F= {(-3,2),(-1,3),(2,1)}
y
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
1 2 3 4 5 6
x
Relations, Domain, and Range
How to illustrate a relation with a “mapping” diagram
F= {(-3,2),(-1,3),(2,1)}
-3
2
-1
3
2
1
Relations, Domain, and Range
Determine domains and ranges from graphs
y
Domain
3
2
1
-1
-2
-3
1 2 3 4 5 6
x
Range
-6 -5 -4 -3 -2 -1
Functions
Definition: A function is a relation in which each element in
the domain corresponds to exactly one element in the range.
Independent variable—element in the domain
Dependent variable—element in the range
Functions
How to check whether a relation is a function
1, check from the set of relation itself
2, vertical line test
y
x
Functions
Function notation:
y=f(x)
Example: f(x)=9x-5
Functions
 See example 6 on page 18
For each function, find f(3)
(a) f(x)=3x-7
(b) The function f depicted by
-2
3
10
6
5
12
(c) The function f defined by the table
x
1
2
3
4
f(x)
-15
-12
-9
-6
Relations, Domain, and Range
(d) The function f depicted by
y
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
1 2 3 4 5 6
x
Homework
PG. 19: 3-78(M3), Supplement
Key problems: 36, 57, 69, S:3