Algebra 1 Common Core Student Edition, Grade 8-9

A f u n c t i o n c a n b e t h o u g h t o f as a r u le t h a t y o u a p p ly t o th e i n p u t i n o r d e r to g e t th e

output. You can describe a nonlinear function w ith words or w ith an equation, just as

y o u d i d w i t h lin e a r f u n c t io n s.

How can you use

reasoning to w rite

a rule?

You can solve a simpler

problem by writing a

rule based on the first

one or tw o rows of the

table. Then see if the rule

works for the other rows.

I W r i t i n g a R u l e t o D e s c r i b e a N o n l i n e a r Fu n c t i o n

The ordered pairs (1,2), (2 ,4 ), (3,8), (4,16), and (5,32) represent a function.

What is a rule that represents this function?

Make a table to organize the x- a n d y - v a lu e s. F o r e a c h r o w , i d e n t i f y r u le s t h a t p r o d u c e

t h e g iv e n y - v a lu e w h e n y o u s u b s t it u t e th e x - v a lu e. L o o k f o r a p a t t e r n i n th e y -v a lu e s.

W h a t rule produces 2, given an x-v a lu e o f 1? The

rules y = 2x, y = x + 1, and y = 2* w o rk fo r (1, 2).

12

2 4

3 8

4 16

5 32

y = x + 1 does n o t w o rk fo r (2, 4). y = 2 x w o rks

fo r (2, 4), b u t n o t fo r (3, 8). y = 2* w orks fo r all

three pairs.

= 2 • 2 • 2 and 16 = 2 • 2 • 2 • 2. The pa tte rn o f

the y-values matches 21, 22, 23, 24, 25, o r y = 2\

T h e f u n c t i o n c a n b e r e p r e s e n te d b y th e r u le y = 2 *.

& Got It? 3. W h a t is a r u le f o r th e f u n c t i o n r e p r e s e n te d b y th e o r d e r e d p a ir s ( 1 , 1 ) , ( 2 , 4 ) ,

(3,9), (4,16), and (5, 25)?

& Lesso n Ch eck

Do y o u k n o w H OW?

1. G raph th e fu n c tio n repre sen ted b y th e ta b le b e lo w. Is
   th e fu n c tio n linear o r nonlinear?

0 1 234

12 13 14 15 16

2. The ordered pairs (0, - 2 ) , (1 ,1 ), (2, 4), (3, 7), and
   ( 4 , 1 0 ) r e p r e s e n t a f u n c t io n. W h a t is a r u le t h a t
   represents this fu nction?


3. W h ic h r u le c o u ld r e p r e s e n t t h e f u n c t i o n s h o w n b y
   the table below?

0 1234

o -1 -4 -9 -1 6

A.y= x2 B. y = - x 3 c-y =

Do yo u UN DERSTAND?

MATHEMATICAL

PRACTICES

4. Vocabulary Does the graph represent a linear
   function o r a nonlinear function? E xp la in.
   b.


5. Error Analysis A classmate says that
   t h e f u n c t i o n s h o w n b y th e ta b le a t t h e
   r i g h t c a n b e r e p r e s e n te d b y th e r u le
   y = x + 1. D e s c r ib e a n d c o r r e c t y o u r
   c la s s m a te ’s e r ro r.

m

0 1

1 2

2 5

3 10

4 17

0

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