1. 1.2 Relations and Functions

2. Quiz:
Fill in the blank of the following sentences: A relation is a set if ____ pairs.

3. Real Number System
Natural Number(whole number) 1, 2, 3, 4, …,100,…1000,… Integer …, -5, -3, -1, 0, 1, 2, 3, 4, 5,… Rational Number m/n, such as 1, 3, 1/3, ,… Real Number numbers that can be written as decimal numbers

4. Real Number System Real Numbers Rational Numbers Integers
Natural Numbers

5. 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]

6. 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.

7. Relation, Domain and Range
Relation: a set of ordered pairs.
{(a1,b1),(a2,b2),(a3,b3)…}
(x , y)
Domain
Range

8. 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)}

9. Relations, Domain, and Range
How to illustrate a relation by a table F= {(-3,2),(-1,3),(2,1)}
Domain
Range

10. Relations, Domain, and Range
How to illustrate a relation with a graph F= {(-3,2),(-1,3),(2,1)} y x 3 2 1 -1 -2 -3

11. Relations, Domain, and Range
How to illustrate a relation with a “mapping” diagram F= {(-3,2),(-1,3),(2,1)} -3 -1 2 2 3 1

12. Relations, Domain, and Range
Determine domains and ranges from graphs y x 3 2 1 -1 -2 -3
Domain
Range

13. 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

14. Functions
How to check whether a relation is a function 1, check from the set of relation itself 2, vertical line test y x

15. Functions
Function notation: Example: f(x)=9x-5
y=f(x)

16. Functions See example 6 on page 18 For each function, find f(3)
f(x)=3x-7
The function f depicted by
The function f defined by the table -2 3 10 6 5 12 x 1 2 3 4
f(x)
-15
-12 -9 -6

17. Relations, Domain, and Range
(d) The function f depicted by y x 3 2 1 -1 -2 -3

18. Homework
PG. 19: 3-78(M3), Supplement Key problems: 36, 57, 69, S:3