Algebra 1 Common Core Student Edition, Grade 8-9

^ESBHSD W r it in g a N o n l i n ear Funct ion Rule Wnllll>li)lfl5[ RESPON SE

How can drawing a
diagram help you to
write a rule?
A diagram visually
represents information
in the problem. It can
give you a clearer
understanding of how
variables are related.

Geometry Write a function rule for the area of a rectangle whose length is 5 ft more

than its width. What is the area of the rectangle when its width is 9 ft?

Step 1 R e p re s e n t t h e g e n e r a l r e la t io n s h ip f ir s t. T h e

area A o f a rectangle is th e p ro d u c t o f its

le n g th i and its w id th w.

w

( ^

A A = € • w

Step 2 R e v is e th e m o d e l t o s h o w t h a t t h e

le n g t h is 5 f t m o r e t h a n th e w id t h. w

Step 3 U s e th e d ia g r a m i n S te p 2 t o w r it e th e f u n c t i o n r u le. T h e f u n c t i o n r u le

A = (w + 5)ic, o r A = w2 + 5w, represents the rectangle's area.

Substitute 9 for w t o f i n d t h e a re a w h e n t h e w i d t h is 9 ft.

A = 92 + 5(9)

= 81 + 45

= 126

When the width of the rectangle is 9 ft, its area is 126 ft2.

® G o t It? 3. a. W r it e a f u n c t i o n r u le f o r t h e a re a o f a t r ia n g le w h o s e h e ig h t is 4 in. m o r e

t h a n t w ic e th e le n g t h o f its b a s e. W h a t is th e a re a o f th e t r ia n g le w h e n th e

le n g th o f its base is 16 in.?

b. Reasoning G r a p h th e f u n c t i o n r u le f r o m P r o b le m 3. H o w d o y o u k n o w

th e ru le is n o n lin e a r?

1 2 6

Lesso n Ch eck

Do y o u k n o w H OW?

Write a function rule to represent each situation.

1. th e t o t a l c o s t C f o r p p o u n d s o f c o p p e r i f e a c h p o u n d
   costs $3.57


2. the height f i n fe e t, o f a n o b je c t w h e n y o u k n o w th e
   object's height h i n in c h e s


3. the am ount y o f y o u r f r i e n d ’s a llo w a n c e i f th e a m o u n t
   s h e re c e iv e s is $2 m o r e t h a n th e a m o u n t x y o u re c e iv e


4. th e v o lu m e U o f a c u b e - s h a p e d b o x w h o s e e d g e
   le n g th s are 1 in. g re a te r th a n th e d ia m e te r d o f t h e
   b a ll t h a t t h e b o x w i l l h o ld

^ MATHEMATICAL

Do y o u UN DERSTAN D? PRACTICES

5. Vocabulary S u p p o s e y o u w r it e a n e q u a t io n t h a t
   g iv e s a as a f u n c t i o n o f b. W h ic h is th e d e p e n d e n t
   variable and w hich is the independent variable?


6. E rro r A n alys is A w o r k e r h a s d u g 3 h o le s f o r fe n c e
   p o s ts. I t w i l l ta k e 15 m i n t o d ig e a c h a d d it io n a l h o le.
   Y o u r f r ie n d w r it e s th e r u le t = 1 5 n + 3 f o r th e t im e
   t, in m in u te s, re q u ire d to d ig n a d d itio n a l h o le s.
   D e s c r ib e a n d c o r r e c t y o u r f r i e n d ’s e rro r.


7. Reasoning Is th e g ra p h o f a fu n c tio n ru le th a t
   r e la te s a s q u a re 's a re a t o its s id e le n g t h continuous o r
   discrete? E x p l a i n.

264 Chapter 4 An Introduction to Functions