Algebra 1 Common Core Student Edition, Grade 8-9

How can you
tell w hether a
relationship in a
ta b le is a fu n ctio n?
If each input is paired
with exactly one output,
then the relationship is a
function.

Rep r esen t i n g a Li n e ar Fu n ct i o n

Photography The table shows the

relationship between the number of photos

a; you take and the amount of memory y

in megabytes (M B ) left on your cam era’s

mem ory chip. Is the relationship a linear

function? Describe the relationship using

words, an equation, and a graph.

Camera Mem ory

: ;. V : 5 V | f ; /

0 512

1 509

2 506

3 503

The amount of memory left

given the number of pictures

taken, as shown in the table

Other representations that

describe the relationship

Look for a pattern that you can describe

in words to w rite an equation. Make a

graph to show the pattern.

The am ount y o f m e m o r y le f t is u n iq u e ly d e t e r m in e d b y th e n u m b e r x o f p h o to s y o u

take. Y o u ca n see th is in th e ta b le above, w h e re e a ch in p u t v a lu e o f x c o rre s p o n d s to

exactly one output value of y. So y is a function o f x. To d e s c rib e th e re la tio n s h ip , lo o k a t

h o w y c h a n g e s f o r e a c h c h a n g e i n x i n t h e t a b l e b e l o w.

Camera Mem ory

M em ory is 512 MB before

any photos are taken.

The independent

variable x increases

by 1 each time.

emory

y

512

+ 1 y 1

1 509 “

r

The dependent variable

+ l ( j --------------------------- V 3 y decreases by 3 each

(^2) ---------------------------- (^506) Y _ qC tim e x increases by 1.
V 3 503 > ' —
Words
Equation
Graph
T h e a m o u n t o f m e m o r y le f t o n th e c h ip is 5 1 2 m in u s th e q u a n t i t y 3 tim e s th e
num ber of photos taken.
y = 512 - 3x
You can use the table to make a graph. The points lie
o n a l in e , so th e r e la t io n s h ip b e t w e e n t h e n u m b e r o f
p h o t o s t a k e n a n d th e a m o u n t o f m e m o r y r e m a in in g is a
lin e a r fu n c tio n.
Go t I t? 2. a. Is t h e r e la t io n s h ip i n th e t a b le b e lo w a l i n e a r f u n c t io n?
Describe the relationship using words, an equation,
and a graph.
512<»
510
508
506
504
502
500>
D—
nput.X ....... (^0)? (^1 23)
GSB32^8 10 1214
° 0 2 4
Number of Photos
b. Reasoning Does the set of ordered pairs (0, 2), (1, 4), (3, 5), and (1,8)
r e p r e s e n t a l i n e a r f u n c t io n? E x p la in.
242 Chapter 4 An Introduction to Functions