- W riting W h a t a d v a n ta g e ( s ) c a n y o u see o f h a v in g a r u le in s te a d o f a t a b le o f v a lu e s
t o r e p r e s e n t a f u n c t io n? - History of M ath T h e g o ld e n r a t io h a s b e e n s t u d ie d a n d u s e d b y m a t h e m a t ic ia n s
a n d a r tis ts f o r m o r e t h a n 2 0 0 0 y e a rs. A g o ld e n re c ta n g le , c o n s t r u c t e d u s in g th e
g o ld e n r a tio , h a s a le n g t h a b o u t 1.6 t im e s its w id t h. W r it e a r u le f o r t h e a re a o f a
g o ld e n r e c ta n g le as a f u n c t i o n o f its w id t h. - Whales F r o m a n e le v a t io n o f 3 .5 m b e lo w th e s u rfa c e o f t h e w a te r, a n o r t h e r n
b o tt le n o s e w h a le d iv e s a t a ra te o f 1.8 m / s. W r it e a r u le t h a t g iv e s t h e w h a le 's d e p t h
d as a f u n c t i o n o f t im e i n m in u t e s. W h a t is th e w h a le ’s d e p t h a fte r 4 m in?
2 6. T h in k A b o u t a P lan The height h, i n in c h e s , o f th e j u ic e i n t h e p it c h e r s h o w n
a t t h e r i g h t is a f u n c t i o n o f th e a m o u n t o f ju ic e j, i n o u n c e s , t h a t h a s b e e n
p o u r e d o u t o f t h e p itc h e r. W r it e a f u n c t i o n r u le t h a t r e p r e s e n ts t h is s it u a t io n.
W h a t is th e h e ig h t o f th e ju ic e a fte r 4 7 o z h a v e b e e n p o u r e d o u t?- W h a t is th e h e ig h t o f th e ju ic e w h e n h a l f o f i t h a s b e e n p o u r e d o u t?
- W h a t f r a c t io n o f th e j u ic e w o u ld y o u p o u r o u t t o m a k e th e h e ig h t d e c re a s e
by 1 in.?
- Tips Y o u g o t o d i n n e r a n d d e c id e to le a v e a 15% t i p f o r t h e s e rv e r. Y o u h a d
$ 5 5 w h e n y o u e n te r e d t h e r e s ta u r a n t.
a. M a k e a t a b le s h o w in g h o w m u c h m o n e y y o u w o u ld h a v e l e f t a fte r b u y in g a
m e a l t h a t c o s ts $ 1 5 , $2 1 , $2 4 , o r $ 3 0.
b. W r it e a f u n c t i o n r u le f o r th e a m o u n t o f m o n e y m y o u w o u ld h a v e le f t i f th e
meal costs c d o l l a r s b e f o r e t h e t i p.
c. G r a p h t h e f u n c t i o n r u le. - Car Rental A c a r r e n t a l a g e n c y c h a rg e s $ 29 p e r d a y t o r e n t a c a r a n d $ 1 3 .9 5 p e r d a y
f o r a g lo b a l p o s it io n in g s y s te m (G P S ). C u s to m e r s a re c h a r g e d f o r t h e i r f u l l t a n k o f
gas a t $ 3 .8 0 p e r g a llo n.
a. A c a r h a s a 1 2 -g a l t a n k a n d a GPS. W r it e a r u le f o r t h e t o t a l b i l l b as a fu n c tio n o f
th e n u m b e r o f days d th e c a r is r e n te d.
b. W h a t is th e b i l l f o r a 9 - d a y re n ta l? - Projectors Y o u c o n s u lt y o u r n e w p r o j e c t o r ’s i n s t r u c t i o n
m a n u a l b e fo r e m o u n t i n g i t o n t h e w a ll. T h e m a n u a l says to
m u l t i p l y th e d e s ir e d im a g e w i d t h b y 1.8 t o f i n d t h e c o r r e c t
distance o f the projector lens from the w all.
a. W r it e a r u le t o d e s c r ib e t h e d is ta n c e o f th e le n s f r o m th e w a ll
as a fu n c tio n o f d e s ire d im a g e w id th.
b. T h e d ia g r a m s h o w s t h e r o o m i n w h ic h th e p r o je c t o r w i l l
b e in s t a lle d. W i l l y o u b e a b le to p r o je c t a n im a g e 7 f t
wide? Explain.
c. W h a t is t h e m a x im u m im a g e w i d t h y o u c a n p r o je c t i n t h e ro o m? - Reasoning W r it e a r u le t h a t is a n e x a m p le o f a n o n lin e a r f u n c t i o n t h a t f it s th e
fo llo w in g description.
When d is 4, r i s 9 , a n d r is a f u n c t i o n o f d.
volum e = 64 oz-12 f t -10 in.I ft266 Chapter 4 An Introduction to Functions