0
What’s my
rule?
5
Input
(x)
output
(y)
0
5
1
What’s my
rule?
6
Input
(x)
output
(y)
0
5
1
6
What’s my
rule?
2
7
Input
(x)
output
(y)
0
5
1
2
6
7
What’s my
rule?
3
?
Input
(x)
output
(y)
0
5
1
2
3
6
7
Today, we are
going to learn
how to use
algebraic
expressions and
properties to
analyze numeric
and geometric
patterns – SPI
6.3.7
You are going to
make some
notations in
your journals.
Snoopy’s
Journal
My Function Machine takes a value
called input and performs one or more
operations on it according to a “rule”
to produce a new value called the
output.
A function is a relation
that assigns exactly one
output value to one
input value
You can organize the
input-output values
of a function in a
function table.
Input
(x)
output
(y)
0
1
2
3
5
6
7
8
The function rule describes the
relationship between each input
and output.
Add 5
Input
(x)
output
(y)
0
1
2
3
5
6
7
8
I can use an algebraic expression to
represent the rule of my function
machine
0
X+5
5
You can also use a “rule” to
describe a pattern in a
+8
sequence of numbers.
For example: 8, 16, 24, 32, …
A sequence is a list of
numbers in a specific order.
What rule would you use for
the above sequence?
Each number in a list is called a
term of the sequence.
An Arithmetic sequence can be
found by adding the same
number to the previous term.
8, 16, 24, 32, …
+8
+8
+8
In a Geometric Sequence, each
term is found by multiplying
the previous term by the same
number.
For example:
2, 10, 50, 250, …
x5
x5
x5
You can also write an
algebraic expression to
describe a sequence.
The value of each term
can be described as a
function of its
position in the
sequence.
X+5
Who uses
patterns
and
functions?
Functions are used in
business to show costs.
For example:
Snoopytronics Inc. needs
to hire a company to
monitor employee
computer activity.
The cost is $4 per
computer.
If we make a table of input and
output values of cost per
computer, it would look like this:
Input
(x)
output
(y)
1
4
2
8
3
12
4
16
Hmmm, I
wonder
what the
rule would
be…
Scientists use
look for
patterns when
they do
experiments.
There are patterns in music.
There are
patterns in
art.
There are patterns in nature.
Can you think of
other places we find
patterns?
Now,
let’s try
some
examples!
What’s
the rule ?
Correct! Multiply by 8, or 8x
What’s the
missing
term?
Correct!
0
What’s the
rule for
this one?
Correct!
Divide by 2,
x
or /2
input(x)
output(y)
0
7
1
9
2
11
3
13
2x + 7
Sometimes
the rule can
have 2 steps!
Correct! 4x + 1
input(x)
output(y)
?
0
1
1
5
2
9
3
13
See if you can
guess the 2step rule.
Now, let’s
play a game
to see if you
can guess the
rule!
Now, you create a rule and
matching function table and
explain how you would find the
input, given the rule and output
values. Write it in your journal.