warm-up: evaluating functions

Evaluate the following:

1. For f(4)

2. For f(-3)

3. For f(-9)

2( ) 2 5f x x x

CCGPS Acc. Algebra

UNIT QUESTION: How do we graph functions, and what can be done to change the way they look?Standard: MM1A1

Essential Question:How do we write the function to represent a sequence?Standard: MM1A1f

Sequences• 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.

Contest

Monday: $150

Tuesday: $300

Wednesday: $450

Thursday: $600

Friday: $750

Sequences

These prize amounts form a sequence.

Sequence: A function whose domain is a set of consecutive whole numbers.

What would be the value on Day 6? Day 7?

SequencesThe values in the range are called the terms of the sequence.

Domain: 1 2 3 4…....n

Range: a1 a2 a3 a4….. an

A sequence can be specified by an equation or rule.

Contest

a1 $150

a2 $300

a3 $450

a4 $600

a5 $750an represents a general term where n can be any number. What is the closed formula for an?

Sequences

Sequences can continue forever. We can calculate as many terms as we want as long as we know the rule or equation for an.

Example:

2, 8, 14, 20, ___ , ___,……. _____ .

an = 6n - 4

Writing Terms of a Sequence

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

Practice

an = -5n + 20

Find a1, a2, a3, a4, a5

a1 = First Term

a2 = Second Term

a3 = Third Term

a4 = Fourth Term

a5 = Fifth Term

15

10

5

0

-5

4251 3

0011 0010 1010 1101 0001 0100 1011 1 1na a d n

Writing Rules Using the Formula:an = a1+ d(n-1)

a1 = 3 First Term

a2 = 5 Second Term

a3 = 7 Third Term

a4 = 9 Fourth Term

an = nth Term

What is the rule? an = ???

an= 3 + 2(n-1)

an= 3 + 2n – 2 = 2n + 1

Writing Rules for a Sequence

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

Writing Rules for a Sequence

a1 = 7 First Term

a2 = 4 Second Term

a3 = 1 Third Term

a4 = -2 Fourth Term

an = ?? nth Term

What is the rule? an = ???

Try This!

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

4251 3

0011 0010 1010 1101 0001 0100 1011

EOCT Practice

a) 77 b) 81

c) 84 d) 86b

4251 3

0011 0010 1010 1101 0001 0100 1011

EOCT PracticeFind the 25th term of the sequence 7, 11, 15, 19, 23, ...

a) 103 b) 104

c) 107 d) 111a

Classwork/Homework• Sequence Practice Worksheet• You’re Toast, Dude! Task