1. Bellwork: Match the following graphs with their equations. NO CALCS! y=-x 2 X=# x=y 2 x = -y 2 1. 2.3. 4. 5. 6. 7. 8. 9.10.11. 12.

2. Unit 1 – Day1

3. Essential Question  What is a function?  How can you tell if a relation is a function?  How do you simplify function notation?  Where do you see functions in real life?

4. Basic Graphs y=-x 2 X=# x=y 2 x = -y 2

5. Step Functions  Also known as the greatest integer function is denoted by [[x]]. [[-2]] = [[-0.5]] = [[1]] = [[-1.5]] = [[0]] = [[1.5]] = [[-1]] = [[0.5]] = [[2]] = -2 1 -2 0 1 0 2

6. 1.1 Functions  Function: A relation that assigns every element in set D (Domain) to only one element in set R (Range). (x’s do not repeat!)  Example1: Determine whether each relation represents a function. X22345 y1110851 a. b. c.{(1, 3) (2, -5) (7, 3)} d. {(1, 7) (2, -3) (1, -4)} e. f. NO YES NO YES

7. Vertical Line Test: If a graph is a function a vertical line will only cross the graph once. Example2: Are the graphs functions? a. b. c. d. e. f. NO YES NO YES NO

8. Domain: the set of x values of a function. Example 3: Find the domain of each function. a. {(-3, 0) (-1, 4) (0, 2) (2, 2) (4, 1)} b. g(x) = -3x 2 + 4x + 5 d. e. D:{-3, -1, 0, 2, 4} D:(-∞,∞) D: (- ∞, -5) U (-5, ∞) D: (-∞, 4/3] c. D: (-∞, -6) U (-6, 6) U (6, ∞) f. D: [-2/5, ∞)

9. Piecewise-Defined Functions  Example 4: Sketch the graph

10. Example 4 continued  B.)  C.)

11. Example 5: Evaluate using function notation let g(x) = -x 2 +4x+1 and find a.g(2)b. g(t)c. g(x+2) d. g(-5) e. g(3x)

12. Example 6: Evaluate the function when x = -1, 0, and 1. a. f(-1) = 2 b. f(0)=-1 c. f(1) = 0

13. HW 9/5  P. 82-84 #6,8,32, 33, 66,68,70  P. 96 #72 (graph as a piecewise, ignore other directions)

14. HW  Pg 82  32- 36even  Pg 97  #44 (graph by hand, not in calculator)

15. HW Answers  6. no  8. yes  66. D: (-  66. D: (- ∞, 0) U (0, 2) U (2, ∞)  68. D: (-6,  68. D: (-6, ∞)  70. D: (- (3,  70. D: (- ∞, -3) U (3, ∞)