Algebra 1 Common Core Student Edition, Grade 8-9

Formalizing Relations

and Functions

Common Core State Standards

F-IF.A.1 Understand th a t a fu nction from one set (called

the dom ain) to another set (called the range) assigns to

each elem ent o f th e dom ain exactly one elem ent o f the

range... Also F-IF.A.2

MP 1, MP 27 M P 3 , M P 4 , MP 6

Object ives T o d e t e r m in e w h e t h e r a r e la t io n is a f u n c t i o n

T o f i n d d o m a in a n d r a n g e a n d u s e f u n c t i o n n o t a t io n

Where you land is

related to where

you s ta rt.

MATHEMATICAL

PRACTI CES

r—

11 " j G e t t i n g R e a d y!

Yo u r f r i e n d i s p l ayi n g

a b o ard gam e. He is

on t h e space shown

in t he diagram at t he

right. He rolled a 3

to get to that space.

Where could he have

st art ed? Explain your

reasoning.

13 1 2 ^

Lose , ,

Turn Move

-4

Roll Move

Again +4

3 4

Lesso n

Vocabulary

relation

• dom ain


• range


• vertical line test


• fu n c tio n
  notation

A relation is a p a irin g o f n u m b e rs in o n e set, c a lle d th e domain, with numbers in

a n o t h e r s et, c a lle d t h e range. A r e la t io n is o f t e n r e p r e s e n te d as a s e t o f o r d e r e d p a ir s

[x, y ). I n t h is case, th e d o m a in is th e s e t o f x - v a lu e s a n d th e r a n g e is th e s e t o f y -v a lu e s.

Esse n t i a l U n d e r st a n d i n g A function is a special type of relation in which each

v a lu e i n th e d o m a in is p a ir e d w i t h e x a c tly o n e v a lu e i n th e ra n g e.

Thinlc^

W h en is a re la tio n

not a function?

A function maps each

domain value to exactly

one range value. So a

relation that maps a

domain value to more

than one range value

cannot be a function.

Ident ifying Functions Using M apping Diagram s

Identify the domain and range of each relation. Represent the relation with a

mapping diagram. Is the relation a function?

Q { ( - 2 , 0. 5 ) , ( 0 , 2. 5 ) , ( 4 , 6. 5 ) , ( 5 , 2. 5 ) }

The dom ain is {-2, 0, 4, 5}.

The range is {0.5, 2.5, 6.5}.

0{(6, 5), (4,3), (6, 4), (5, 8)}

The dom ain is {4, 5, 6 }.

The range is {3,4, 5, 8}.

Domain Range

r .................

Each dom ain

-2 ~—-*► 0. 5 value is m apped

0 ------- 2.5 < 7 } to only one range

4 ^ 6.5 value. The relation

5 f is a fu n c tio n.

The dom ain value

6 is m apped to

tw o range values.

The re la tio n is not

a fu n c tio n.

268 Chapter 4 An Introduction to Functions