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 x 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 3 2 1 -1 -2 -3

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

Relations, Domain, and Range Determine domains and ranges from graphs y x 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 3 2 1 -1 -2 -3 Domain Range

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: Example: f(x)=9x-5 y=f(x)

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

Relations, Domain, and Range (d) The function f depicted by y x 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 3 2 1 -1 -2 -3

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