For each table, determine whether the relationship is a linear function. Then
represent the relationship using words, an equation, and a graph.- M ountain Climbing 12.
Number
of Hours
Climbing, x
Elevation
(ft), y
0 1127
1 1219
2 1311
31403Grocery Bill 13. Gas in Tank
Number of
Soup Cans, x Total Bill, yMiles
Traveled, xGallons
of Gas, y
0 $52.07 01 1.2
1 $ 5 3. 3 6^17 10.2
2 $ 5 4 .6 5^34 9.2
3 $55.94 51 8. 2Apply 14. Gardening Y o u c a n m a k e 5 g a l o f l i q u i d f e r t i l i z e r b y m i x in g 8 ts p o f p o w d e r e d
f e r t i l i z e r w i t h w a te r. R e p r e s e n t th e r e la t io n s h ip b e t w e e n t h e te a s p o o n s o f p o w d e r
u s e d a n d th e g a llo n s o f f e r t i l i z e r m a d e u s in g a ta b le , a n e q u a t io n , a n d a g r a p h. Is
t h e a m o u n t o f f e r t iliz e r m a d e a f u n c t i o n o f th e a m o u n t o f p o w d e r u s e d? E x p la in.- Reasoning G r a p h t h e s e t o f o r d e r e d p a ir s ( - 2 , - 3 ) , (0 , - 1 ) , ( 1 , 0 ) , ( 3 , 2 ) , a n d ( 4 , 4 ).
D e t e r m in e w h e t h e r t h e r e la t io n s h ip is a l in e a r f u n c t io n. E x p la in h o w y o u k n o w. - Think About a Plan Gears are com m on parts in m any types of m achinery. In the
d ia g r a m b e lo w , G e a r A t u r n s i n re s p o n s e t o th e c r a n k in g o f G e a r B. D e s c r ib e th e
relationship betw een the nu m b e r o f turns o f Gear B and the nu m b e r o f turns o f
Gear A. Use words, an equation, and a graph.- W h a t a re th e in d e p e n d e n t a n d d e p e n d e n t v a r ia b le s?
- H ow m uch m ust you tu rn Gear B to get Gear A to go around once?
- Electric Car A n a u to m a k e r m a k e s a c a r t h a t c a n tr a v e l 4 0 m i o n its c h a rg e d b a t t e r y
b e fo re i t b e g in s to u s e gas. T h e n th e c a r tra v e ls 50 m i p e r g a llo n o f gas u s e d. R e p re s e n t
th e r e la t io n s h ip b e tw e e n th e a m o u n t o f gas u s e d a n d t h e d is ta n c e t r a v e le d u s in g a
ta b le , a n e q u a tio n , a n d a g ra p h. Is t o t a l d is ta n c e tr a v e le d a f u n c t io n o f th e a m o u n t o f
gas u s e d? W h a t a re t h e in d e p e n d e n t a n d d e p e n d e n t v a ria b le s? E x p la in. - Reasoning S u p p o s e y o u k n o w th e p e r im e t e r o f n -j
o c ta g o n s a r r a n g e d as s h o w n. W h a t w o u ld y o u d o t o V""i / \ / V7 V7 \
fin d the p e rim e te r if 1 more octagon was added? 1 __)1 ^ J kJxykJ
1 1 1
1 o c t a g o n 2 o c t a g o n s 3 o c t a g o n s
244 Chapter 4 An Introduction to Functions