Algebra 1 Common Core Student Edition, Grade 8-9

When you graph a real-world function rule, choose appropriate intervals for the units

o n th e axes. E v e r y in t e r v a l o n a n a x is s h o u ld r e p r e s e n t t h e s a m e c h a n g e i n v a lu e. I f a ll

t h e d a ta a re n o n n e g a tiv e , s h o w o n ly th e f i r s t q u a d r a n t.

@QSBBGr ap h i n g a Real- W o r ld Funct ion Rule

How do you choose
values for a real-
world independent
variable?
Look for information
about what the values
can be. The independent
variable c in this problem
is limited by the capacity
of the truck, 200 ft3.

Trucking The function rule TV = 146c + 30,000 represents the total weight W, in

pounds, of a concrete mixer truck that carries c cubic feet of concrete. If the capacity of

the truck is about 200 ft3, what is a reasonable graph of the function rule?

Step 1

M a k e a t a b le t o f in d

o r d e r e d p a ir s (c, TV).

The truck can hold 0 to 200 ft3

of concrete. So only c-values

from 0 to 200 are reasonable.

H

W = 146c + 30,000 ' 1 1 1

0 W= 146(0) + 3 0 ,0 0 0 = 3 0 ,0 0 0 (0, 3 0 ,0 0 0 )

50 W = 146(50) + 30,000 = 37,300 (50, 37,300)

100 W= 146(100) + 30,000 = 44,600 (100, 44,600)

150 W= 146(150) + 30,000 = 51,900 (150, 51,900)

200 W = 146(200) + 30,000 = 59,200 (200, 59,200)

Step 2

G r a p h th e o r d e r e d p a ir s f r o m th e ta b le.

TV reaches a lm o s t 6 0,000 lb

So l/V v a lu e s f r o m 0 t o 6 0 ,0 0 0

in grid increm ents o f 10,000

m ake sense.

Truck Weight

-Q

60,000

£ 40,000

| 20,000

+-<<0

o

The c-values go from 0 to 200.

200 is evenly d ivisib le by 25,

so use g rid increm ents o f 25.

All c-values from 0 to 200

m ake sense, so connect

the points. Stop at 200 ft3,

th e capacity o f th e truck.

Concrete (ft

® ^ Got It? 2. a. The function rule W= 8 g + 7 0 0 re p re s e n ts th e t o t a l w e ig h t TV, i n p o u n d s ,

of a spa that contains g g a llo n s o f w a te r. W h a t is a r e a s o n a b le g r a p h o f th e

f u n c t i o n r u le , g iv e n t h a t th e c a p a c it y o f th e s p a is 2 5 0 gal?

b. Reasoning W h a t is th e w e ig h t o f th e s p a w h e n e m p ty? E x p la in.

I n P r o b le m 2, th e t r u c k c o u ld c o n t a in a n y a m o u n t o f c o n c r e te f r o m 0 t o 2 0 0 f t 3, s u c h as

2 7 .3 f t 3 o r 1 0 5 1 f t 3. Y o u c a n c o n n e c t t h e d a ta p o in t s f r o m th e t a b le b e c a u s e a n y p o i n t

between the data points has meaning.

S o m e g r a p h s m a y b e c o m p o s e d o f is o la t e d p o in t s. F o r e x a m p le , i n t h e S o lv e I t y o u

graphed only points that represent printing w hole num bers of photos.

254 Chapter 4 An Introduction to Functions