Transcript Evaluate the following: f(x)  x  2x  5 1. f(4) = 2.

Evaluate the following:
2
f(x)  x  2x  5
1. f(4) =
13
2. f(-3) =
20
3. f(-9) =
104
CCGPS Alg
2/19/2013
UNIT QUESTION: How do we graph
functions, and what can be done to
change the way they look?
Today’s Question:
How do we write the function to
represent a sequence?
CCGPS Alg
2/19/2013
(I.N. p49)
MCC9-12.F.IF.3 Recognize that
sequences are functions, sometimes
defined recursively, whose domain is
a subset of the integers
Sequences
0011 0010 1010 1101 0001 0100 1011
• Everyday a radio station asks a question for
a prize of $150. If the fifth caller does not
answer correctly, the prize money increased
by $150 each day until someone correctly
answers their question.
• Make a list of the prize money for a week
from Monday to Friday if no one gets it
right.
1
2
4
Contest
0011 0010 1010 1101 0001 0100 1011
Monday: $150
Tuesday: $300
Wednesday: $450
Thursday: $600
Friday: $750
1
2
4
Sequences
0011 0010 1010 1101 0001 0100 1011
These prize amounts form a sequence.
1
2
Sequence: A function whose domain is a set
of consecutive natural numbers.
4
What would be the value on Day 6? Day 7?
Sequences
0011 0010 1010 1101 0001 0100 1011
The values in the range are called the terms
of the sequence.
Domain: 1
2
3
4…....n
Range:
a2
a3
a4….. an
a1
1
2
4
A sequence can be specified by an equation or
rule.
Contest
0011 0010 1010 1101 0001 0100 1011
a1
$150
a2
$300
a3
$450
a4
$600
a5
$750
1
2
4
an represents a general term where n can be any
number. What is the closed formula for an?
Sequences
0011 0010 1010 1101 0001 0100 1011
Sequences can continue forever. We can
calculate as many terms as we want as long as
we know the rule or equation for an.
2
4
Example:
2, 8, 14, 20, ___ , ___,……. _____ .
an = 6n - 4
1
Writing Terms of a Sequence
0011 0010 1010 1101 0001 0100 1011
an = 2n – 3
Find a1, a2, a3, a4, a5
a1 = -1
First Term
a2 = 1
Second Term
a3 = 3
Third Term
a4 = 5
Fourth Term
a5 = 7
Fifth Term
1
2
4
Practice
0011 0010 1010 1101 0001 0100 1011
an = -5n + 20
Find a1, a2, a3, a4, a5
a1 =
15
First Term
a2 =
10
Second Term
a3 =
5
Third Term
a4 =
0
Fourth Term
a5 =
-5
Fifth Term
1
2
4
2
1
an  a1  d  n 1
0011 0010 1010 1101 0001 0100 1011
4
Writing Rules Using the Formula:
a1+ d(n-1)
0011 0010 1010 1101 0001 a
0100
n =1011
a1 = 3
First Term
a2 = 5
Second Term
a3 = 7
Third Term
a4 = 9
Fourth Term
an =
nth Term
What is the rule?
1
2
4
an = ???
an= 3 + 2(n-1)
an= 3 + 2n – 2 = 2n + 1
Writing Rules for a Sequence
0011 0010 1010 1101 0001 0100 1011
a1 = 2
First Term
a2 = 6
Second Term
a3 = 10
Third Term
a4 = 14
Fourth Term
an =
nth Term
What is the rule?
an = ???
an= 4n - 2
1
2
4
Writing Rules for a Sequence
0011 0010 1010 1101 0001 0100 1011
a1 = 7
First Term
a2 = 4
Second Term
a3 = 1
Third Term
a4 = -2
Fourth Term
an = ??
nth Term
What is the rule?
an = ???
1
2
4
Try This!
0011 0010 1010 1101 0001 0100 1011
a1 = 5
First Term
a2 = 12
Second Term
a3 = 19
Third Term
a4 = 26
Fourth Term
an =
nth Term
What is the rule?
an = ???
an= 7n - 2
1
2
4
EOCT Practice
a) 771101 0001 0100 1011
0011 0010 1010
c) 84
b) 81
d) 86
1
2
4
b
EOCT Practice
Find the 25th term of the sequence 7, 11, 15, 19, 23, ...
0011 0010 1010 1101
0001 0100 1011
a) 103
c) 107
b) 104
d) 111
1
2
4
a
Homework
0011 0010 1010 1101 0001 0100 1011
• Practice Sequence Worksheet
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2
4