What’s my
rule?
3
?
Input
(x)
output
(y)
0
5
1
2
3
6
7
Today, we are
going to learn
how to generalize
a variety of
patterns to a
symbolic rule
from tables,
graphs, or words
~ SPI 706.1.2
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?
Ad
d
8
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
Time
s
5
X+5
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.
You can show a sequence in a
table. The position of the
number in the sequence is “x”
and the value of each term is “y”
Position (x)
Value (y)
1
5
2
7
3
9
4
11
Notice the value
increases by 2, so the
first part of the rule
would be 2x
If the rule were simply 2x, then the
value for position 1 would be 2, but its
3 more. That means you add 3 to 2x to
get the next term in the sequence.
Position
Value
1
5
2
7
3
9
4
11
Let’s check the rule 2x + 3!
2(1) + 3 = 5; 2(2) + 3 = 7 Yes!
What is the expression for the
sequence in the table below?
Position
1
2
3
4
Value
4
9
14
?
The value goes up by 5,
so its 5x. But the next
term is 1 less, so the
expression is 5x – 1!
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 for each
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…
The rule can
also be written
as an algebraic
equation, such
as y = 4x, where
y is a function
of x.
We can make a graph of this
“rule” by using the x and y as
coordinates.
y = 4x
Input
(x)
output
(y)
1
4
2
8
3
12
4
16
Suppose Snoop’s band recorded a CD. They want to
make copies and sell them. They found a
recording company that charges $250 for
making a master CD and designing the art for
the cover. In addition, they charge $3 to burn
each CD. The total cost of making CD’s depends
on the number of CD’s burned.
Let c = the number of CD’s burned and
t = the total cost. What would be the rule?
Yes! The
rule would
be…
t = 3c +
250
You can also write a rule from a
graph using the coordinates!
Hint: make
a table!
Input
(x)
output
(y)
0
-1
1
1
2
3
3
5
Y = 2x-1
Now,
let’s try
some
examples!
What is the
rule for the
table below?
Correct! 5x
Which equation fits
the table?
A. y = x + 15
B. y = 10x + 5
C. y = 3x + 12
D. y = 15x
What’s the
rule for
this one?
Correct!
Divide by 2,
or
y=
1/
2x
What is the rule for the
sequence in the table below?
Position (x)
1
2
3
4
Value (y)
13
21
29
37
Correct! 8x + 5
input(x)
output(y)
0
7
1
9
2
11
3
13
What would
be the value
for y if x = 4?
X = 15
Correct! y = 4x + 1
input(x)
output(y)
?
0
1
1
5
2
9
3
13
See if you can
guess the
rule.
Can you guess the rule?
I’ll give you a hint ~ make a table!
input(x)
output(y)
1
0
2
2
3
4
4
?
Snoopy is thinking of
joining a health club.
It charges a one-time
membership fee of
$30 plus a monthly
fee of $12.
Write a rule for the
total charge (y) for
the number of
months (x) Snoopy
Correct! y = 12x + 30
goes.
I need to
workout.
Now, it’s your turn to create a
real-world problem with a rule, a
matching function table, and a
coordinate graph of the rule. Write
it in your journal.