input (x) output (y) 0 5 16 27 3 ? 3 what’s my rule?
TRANSCRIPT
Input(x)
output(y)
0 5
1 62 7
3?
3
What’s my
rule?
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 valueYou can
organize the input-output values of a function in a function table.
Input(x)
output(y)
123
0 5678
The function rule describes the
relationship between each input and output.
Input(x)
output(y)
12
0 567
3 8
Add 5
I can use an algebraic expression to represent the rule of my function
machine0
5
X + 5
You can also use a “rule” to describe a
pattern in a 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?
+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
Add8
In a Geometric Sequence, each term is found by multiplying the
previous term by the same number.
For example:2, 10, 50, 250, … x
5 x 5 x 5
Times5
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
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) 1 2 3 4
Value (y) 5 7 9 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 1 2 3 4
Value 5 7 9 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
2
3
4 16
4
8
12
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.
Input(x)
output(y)
1
2
3
4 16
12
8
4
y = 4xInput
(x)output(y)
1
2
3
4 16
12
8
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!Input
(x)output(y)
0 -1
1 1
2 3
3 5
Y = 2x-1
Hint: make a table!
Now, let’s try
some exampl
es!
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 = 1/2
x
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
What would be the value for y if x
= 4?
input(x)
output(y)
0
1
2
3
7
9
11
13 X = 15
input(x)
output(y)?
0
1
2
3
See if you can guess the rule.
1
5
9
13
Correct! y = 4x + 1
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 goes.
I need to workout.
Correct! y = 12x + 30
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.