Algebra 1 Common Core Student Edition, Grade 8-9

@ C om m on C ore State Standards

\A /rItir » n n F l ir» r'tir\n P i I N-Q.A.2 Define appropriate quantities fo r th e purpose

VVM IIIIU U I UllkJIk-MI IXUIC of descriptive modeling Also A-SSE.A.1 a, A-CED.A.2

MP 1, MP 2, MP 3, MP 4

Object ive T o w r it e e q u a tio n s t h a t r e p r e s e n t f u n c t io n s

Start with a

simple case—how

fa r has your

frie n d swum when

you fin is h your

■f i rc+ I nrtO

MATHEMATICAL

PRACTICES

cS^E/>| ' Getting Ready!

n

Yo u an d a f r i e n d a r e sw i m m i n g 2 0 l a p s a t t h e l o c a l p o o l. O n e l ap i s t h e

dist ance across t he pool and b ack. You both swim at t he same r at e.

Yo u r f r i e n d st a r t e d f i r s t. Th e t r a i l o f a r r o w s sh o w s how f a r h e h as

alread y swum. W hat equation gives t he distance you have swum as a

function of the number of laps your friend has swum? How far have

you swum when yo ur f r i en d f in i sh es? Exp lain yo ur reasoning.

In the Solve It, you can see h o w the value o f one variable depends on another. O nce you

see a p a tte rn in a re la tio n s h ip , y o u can w rite a ru le.

Essent ial Und er st and ing Many real-world functional relationships can be

r e p r e s e n te d b y e q u a tio n s. Y o u c a n u s e a n e q u a t io n to f i n d th e s o lu t io n o f a g iv e n

r e a l- w o r ld p r o b le m.

Think .-

How can a model

help you visualize a

real-w orld situation?

Use a model like the

one below to represent

the relationship that is

described.

r

1

4 ° -fc.o

Writing a Function Rule

Insects You can estimate the tem perature by counting the number of chirps

of the snowy tree cricket. The outdoor temperature is about 40°F more than

one fourth the number of chirps the cricket makes in one minute. What is a

function rule that represents this situation?

Relate te m p e ra tu re is 40°F m o re th a n | o f the n u m b e r o f ch irp s in 1 m in

Define Let T = the temperature. Let n = the nu m b e r o f chirps in 1 m in.

Write 40

A f u n c t i o n r u le t h a t re p r e s e n ts t h is s it u a t io n is T = 4 0 + \n.

262 Chapter 4 An Introduction to Functions

LiLi-l