1.2 Represent Functions as Rules and Tables

EQ: How do I represent functions as rules and tables??

Warm UP!!!!Solve the following for x

1. X + 7 = 15

2. X – 3 = 25

3. X + 14 = -10

Vocabulary

• Relation: is a set of ordered pairs. • Domain: is the set of the first members of

each of the ordered pair (input)• Range: is the set of the second member of

each of the ordered pairs. (output)• Function: a relation is a function if “for every

element in the domain there is exactly one element in the range.”

What is the Domain and Range in the following.

1. ( 1,3) (4,5) ( 6,7) (10, 12)2. (-2, 0 ) ( 14, 32) ( 23, 57) ( 99, 100)3. ( 3, 45) ( 56, 77) ( 1000, 1010) ( 1220, 1344)4. (@, #) ( $, %) ( ^, & ) ( !, *)

The domain and range are also called input and output

The input variable is called an independent variable

The output variable is called the dependent variable, because its value depends on the value of the input variable.

Find the range of the relation.

1. Y = 2x + 2 Domain ( 1, 2,3,4)2. Y = 3x Domain ( 3,4,5,6)3. Y – x = 1 Domain ( 1,2,3,4)

Functions: Some relations are also functions. A relation is a function if for “every element in the domain there is exactly one element in the range.”In other words, for each value of “x” there is a unique value for “y”

Determine whether the ordered pairs of numbers below represent a function.

1. ( 1, 2 ) (3, 4) ( 5, 6) ( 7, 8)2. ( 3, 4) ( 5, 6) ( 9, 10) ( 3, 8)3. ( 14, -15) ( 23, 10) ( 34, 10)

Function Notation: is used to represent relations which are functions. Some commonly used letters to represent functions include

f, g, h, F, G, and H.

Example: f(x) = 2x + 1; find f(3)

g(x) = 4- 2x2; find g(2)

Classwork: Complete the following # 1- 20.