Algebra 1 Common Core Student Edition, Grade 8-9

—— B—

a function.

/

03 1 ' Getting Ready!

Number

of Steps

Number

of Blocks

Ordered

Pair

Th e t ab le shows t he relat io nship bet ween

the number of steps in the staircase below

and t h e number o f b lo cks needed t o build

t he st aircase. Copy and complete t he t ab le.

Is the relationship a function? I f so, is it a

linear funct ion? Exp lain.

Langua ge is

im portant! M ake

sure you know

th e d e fin itio n o f

MATHEMATICAL

PRACTICES

Patterns and

Nonlinear Functions

@ Common Core State Standards

A-REI.D.10 Understand that the graph of an equation

in tw o variables is the set o f all its solutions plotted in

the coordinate plane, often fo rm in g a curve (which could

be a line). Also F-IF.B.4

MP 1, MP 2, MP 3, MP 4, MP 6

Object ive T o id e n t i f y a n d r e p r e s e n t p a t t e r n s t h a t d e s c r ib e n o n lin e a r f u n c t io n s

^ Lesson t

Vocabulary

• nonlinear
  fu n ctio n

The relationship in the Solve It is an exam ple o f a nonlinear function. A

nonlinear function is a f u n c t i o n w h o s e g r a p h is n o t a l in e o r p a r t o f a lin e.

Esse n t i a l U n d e r st a n d i n g Just like lin e a r fu n ctio n s, n o n lin e a r fu n c tio n s can be

r e p r e s e n te d u s in g w o r d s , ta b le s , e q u a tio n s , se ts o f o r d e r e d p a ir s , a n d g ra p h s.

Concep t Su m m ar y Linear and Nonlinear Functions

Linear Function

A l i n e a r f u n c t i o n is a f u n c t i o n w h o s e

g r a p h is a n o n v e r t ic a l lin e o r p a r t o f a

nonvertical line.^0

Nonlinear Function

A n o n lin e a r f u n c t i o n is a f u n c t io n

w h o s e g r a p h is n o t a lin e o r p a r t o f

a lin e.

0

7

y

X

0

0.

246 Chapter 4 An Introduction to Functions