Go t I t? 3. Graph each function rule. Is the graph continuous o r discrete? J u s t i f y
your answer.
a. The amount of water w i n a w a d i n g p o o l , i n g a l l o n s , d e p e n d s o n t h e
am ount of tim e t, i n m in u t e s , th e w a d in g p o o l h a s b e e n f i l li n g , as r e la te d
by the function rule w = 3t.
b. T h e c o s t C f o r b a s e b a ll tic k e ts , i n d o lla r s , d e p e n d s o n t h e n u m b e r n o f
tic k e ts b o u g h t , as r e la t e d b y th e f u n c t i o n r u le C = 16 n.What input values
make sense for these
nonlinear functions?
Include 0 as well as
negative and positive
values so that you can
see how the graphs
change.
T h e f u n c t i o n r u le s g r a p h e d i n P r o b le m s 1 - 3 r e p r e s e n t l i n e a r f u n c t io n s. Y o u c a n a ls o
g r a p h a n o n lin e a r f u n c t i o n r u le. W h e n a f u n c t i o n r u le d o e s n o t r e p r e s e n t a r e a l- w o r ld
situation, graph it as a continuous function.Gr ap h in g N o n lin ear Funct ion Rules
What is the graph of each function rule?
Qy = |x| - 4
Step 1
M a k e a t a b le o f v a lu e s.-4
II J_ 1 II O
(-4, 0)
-2 y = 1—2| - 4 = -2 (-2, -2)(^0) y = |0| — 4 = —4 (0, - 4 )
(^2) y = |2| - 4 = - 2 (2, - 2)
4
II 1 II o
(4, 0)
0y =x2 + 1
Step 1
Make a table of values.
-2 y = (-2)2 + 1 = 5 ( - 2 , 5)
-1 y = (-1 )2 + 1 = 2 ( - 1 , 2)
o IIohO+ II (0,1)
1 y = 12 + y = 2 (1,2)
2 y = 2 2 + 1 = 5 (2, 5)
G o t It? 4. W h a t is th e g r a p h o f th e f u n c t i o n r u le y = x 3 + 1?
Step 2
G r a p h th e o r d e r e d p a ir s.
Connect the points.
Step 2
G r a p h t h e o r d e r e d p a ir s.
C o n n e c t th e p o in ts.
2 5 6 Chapter 4 An Introduction to Functions