Algebra 1 Common Core Student Edition, Grade 8-9

How can you use a

pattern to complete

the table?

You can draw figures

with 4 and 5 blocks on

an edge. Then analyze

the figures to determine

the total number of

blocks they contain.

Pr o b l em 2 Rep r esen t i n g Pat t er n s an d N o n l i n ear Fu n ct i o n s

The table shows the total number of blocks

in each figure below as a function of the

number of blocks on one edge.

0

1 2 3

What is a pattern you can use to complete

the table? Represent the relationship using

words, an equation, and a graph.

D r a w th e n e x t t w o fig u r e s to c o m p le t e th e ta b le.

/ / // /

/

/

/// //-

/ /■ /■ X y

A cube w ith 4 blocks on an edge contains

4 • 4 • 4 = 64 blocks. A cube w ith 5 blocks

on an edge contains 5 • 5 • 5 = 125 blocks.

1

2

3

4

5

Number

ocks, y

Ordered

Pair (x, y

(^1) (1,1)
8 (2, 8)
(^27) (3, 27)
». j m
■■
tra in lllllli
Hf»i to fW ?{.!■ ■3HiTPiffj ■
(^11) (1,1)
2 8 (2,8)
(^327) (3, 27)
(^464) (4, 64)
5 125 (5,125)
Words
Equation
The total num ber o f blocks y is t h e c u b e o f t h e n u m b e r
of blocks on one edge x.
You can use the table to make a graph. The points do not lie on a line. So
th e r e la t io n s h ip b e t w e e n t h e n u m b e r o f b lo c k s o n o n e e d g e a n d th e t o t a l
n u m b e r o f b lo c k s is a n o n lin e a r f u n c t io n.
150
100
50
<9 Got It? 2. The table shows the num ber o f new branches in each figure o f the pattern
b e lo w. W h a t is a p a t t e r n y o u c a n u s e t o c o m p le t e th e ta b le? R e p r e s e n t th e
r e la t io n s h ip u s in g w o r d s , a n e q u a t io n , a n d a g ra p h.
Number of
Figure, x^12
h m
(^34 5)
Number of
New Branches, y^39 : :^27 m. | u I
2 4 8 Chapter 4 An Introduction to Functions