1. 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.

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

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

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

5. 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

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

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

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

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

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

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

12. 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

13. 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)

14. 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.

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

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

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

18. 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

19. 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.