Relations/Sequences Objective: Students will learn how to identify if a relation is a function. They will also be able to create a variable expression.

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Presentation transcript:

Relations/Sequences Objective: Students will learn how to identify if a relation is a function. They will also be able to create a variable expression and evaluate a sequence for a given term.

Information Relation: pairing of numbers in a set. Domain: x coordinate, input, independent Range: y coordinate, output, dependent

Identify range and domain (2,1) (2,5) (-2,7) (5,4) (-1,6)(-4, -1)(6,5)(-1,4)

Identify range and domain-st (3,5)(-1,2)(2,4)(1,-9) (8,3)(8,6)(8,9)(3,3)

Functions Function: input (x) has exactly one output (y). 2 ways to tell if function Mapping diagram Vertical line test Vertical line test: vertical line passes through 2 points; not function

Function-map diagram (-1,-2)(-1,2)(3,1)(1,1) (-2,-3)(2,1)(0,-3)(1,2)

Function-map diagram-st (0,12)(2,1)(3,2)(12,0) (4,0)(2,1)(-3,0)(4,9)

Function-vertical line test (-4,-2)(0,3)(-1,-2)(3,3) (-2,0)(-1,-2)(3,1)(3,-2)

Function-vertical line test-st (1,3)(2,4)(-2,4)(1,-5) (1,2)(4,5)(3,-1)(2,-3)

x -4 -4 -1 3 4 y -5 -4 -3 2 0 x 0 0 2 4 8 y -3 -1 1 3 -1 (5,0), (6,0), (7,6), (8,8), (8,10) (-6,4), (-3,0), (4,2), (4,3), (7,9)

Information Function notation: remove y, replace with f(x) f(x) means f of x

Function Notation Given g(x) = 4x – 5. Find values. g(x) when x = 2 g(-10) x when g(x) = 19 g(x) when x = -1

Function Notation Given f(x) = -3x + 1. Find values. f(x) when x = -1 f(x) when x = 5 x when f(x) = -17 f(-20)

Notes Sequence: ordered list of numbers. Term: each number of a sequence. Arithmetic sequence: difference between two consecutive number is the same. Ex: 2, 4, 6, 8 Difference is ___? Common Difference: difference between the numbers.

DESCRIBE SEQUENCE with words 10, 11, 12, 13 5, 10, 15, 20

Describe sequence with words. 12, 17, 22, 27, 32 5, 3, 1, -1, -3 15, 11, 7, 3, -1 52, 61, 70, 79

Write an expression and Find the term 18, 36, 54, 72: Find the 7th term. 64, 67, 70, 73; Find the 10th term.

Write an expression and Find a term in the sequence 3, 8, 13, 18; Find the 10th term 20, 33, 46, 59: Find the 17th term 29, 38, 47, 56; Find the 15th term. 101, 103, 105, 107: Find the 30th term

Review Objective: Students will learn how to identify if a relation is a function. They will also be able to create a variable expression and evaluate a sequence for a given term.