SEQUENCES as Functions Trivia Question How many states

SEQUENCES as Functions

Trivia Question • How many states border the Gulf of Mexico? a) 3 b) 4 c) 5 d) 6 e) 7

Trivia Question • How many states border the Gulf of Mexico? a) 3 b) 4 c) 5 d) 6 e) 7

Trivia Question • The actor Johnny Depp (Pirates of the Caribbean) is afraid of what? a) trains b) clowns c) flying d) spiders e) public speaking

Trivia Question • The actor Johnny Depp (Pirates of the Caribbean) is afraid of what? a) trains b)clowns c) flying d) spiders e) public speaking

Definition of Sequences • First, let’s look at a few and try to determine the pattern: – A. – B. – C. – E. – F. – G. 5, 4, 3, 2, 1 S, M, T, W, T, F, S 1, 2, 3, 4, 5, …, 99, 100 4, 7, 10, 13, 16, … 10, 1000, 100000, … 95, 91, 87, 83, 79, 75…

What does this have to do with Functions? ? ? x f(x) 1 2 3 4 5 6 Remember this? Writing an equation from a table? We know this as a linear function. . but it is also called an arithmetic sequence.

Think of it like this…. • Each number is like a person standing in line. • These are the numbers in line: 4, 8, 12, 16, 20, 24, 28; this is the range of the function. • The number’s place in line - 1 st in line, 2 nd in line, 3 rd in line, etc. ; this is the domain. 4 8 12 16 20

• The first number in line is 4; the ordered pair is (1, 4). • The second number in line is 8; the ordered pair is (2, 8). • Get it? x 1 2 3 4 5 6 7 y 4 8 12 16 20 24 28 4 8 12 16 20

Wait. . how do we write an equation from a table? • Write the equation in y = mx + b. • m = slope…how do we find the slope in a table? ___________ • b = y-intercept…how do we find the yintercept in a table? ________________________

So, in relation to functions, a sequence is a function whose domain is a consecutive set of whole numbers, usually beginning with 1. The range is the terms of the sequence. Domain 1 2 3 4…. . n Range a 2 a 3 a 4. . . an a 1

Arithmetic Sequence To be arithmetic, the sequence must have • Find the common difference (slope) a common in this sequence: difference between consecutive terms in the sequence. 4, 8, 12, 16, 20, 24 This difference is the rate of change, or The common slope, of the linear function. difference is ___.

Let’s try it! 1, 2, 3, 4, 5, … Make a table of values: X (place in line) y (number)

Your table should look like this: X 1 2 3 4 5 (place in line) y (number)

X 1 2 3 4 5 (place in line) y (number) What is the slope? _____ What is the y-intercept? ______ What is the equation? ______

X 1 2 3 4 5 (place in line) y (number) What is the slope? 1/1 = 1 What is the y-intercept? 0 What is the equation? y = x

Trivia Question • How long does it take the sun’s rays to reach the Earth? a) 8 min, 18 sec b) 10 min, 18 sec c) 12 min, 18 sec d) 8 min, 8 sec e) 8 min, 28 sec

Trivia Question • How long does it take the sun’s rays to reach the Earth? a) 8 min, 18 sec b) c) d) e) 10 min, 18 sec 12 min, 18 sec 8 min, 28 sec

Let’s try another one! 5, 10, 15, 20, 25… Make a table of values: X (place in line) y (number)

X 1 2 3 4 5 5 10 15 20 25 (place in line) y (number) What is the slope? _____ What is the y-intercept? ______ What is the equation? ______

Let’s try another one! 4, 7, 10, 13, 16… Make a table of values: X (place in line) y (number)

X 1 2 3 4 5 4 7 10 13 16 (place in line) y (number) What is the slope? _____ What is the y-intercept? ______ What is the equation? ______

Let’s review: What is another word for sequence? pattern

Let’s review: The pattern is the same thing as the…? slope

Let’s review: How do we turn a List 1 -5 in domain sequence into Put sequence in a table? range

Let’s review: How do we turn a table into an equation? Find slope Find yintercept

Trivia Question • Which country has the most tractors per capita? a) U. S. b) Germany c) Japan d) Australia e) Iceland

Trivia Question • Which country has the most tractors per capita? a) U. S. b) Germany c) Japan d) Australia e) Iceland

What do they mean? • Sequence • Pattern • Function • Domain • Range