2. World 2-1 Functions, Relations, Domain and Range

3. Recall that a FUNCTION takes 1 input and produces only 1 output for that exact input. Mr. Function A RELATION, takes 1 input, but may produce multiple outputs for that given input. Ms. Relation Function Notation f(x) = 4x +10 output input (x, f(x) )

4. (1) Graph - Vertical Line Test Function ____ Function _____ A vertical line touches the curve at ONLY 1 spot at a time YES NO A vertical line touches MORE THAN 1 spot at a time. Function Relation

5. (2) Table of Values Each x value has only ONE y value. An x value has MORE THAN ONE y value x y 02 14 36 58 x y 10 21 43 45 Function ____ YES Function ____ NO Function Relation

6. (3) Mapping Diagram YES NO Function ____ AB f 2 3 5 7 4 6 10 14 SourceTarget Each source value has only ONE target value Function ____ AB r 2 3 5 7 4 6 10 11 A source value has MORE THAN ONE target value Function Relation

7. Ex. 1 Calculate the output value of each function

8. Not every x value can be inputted into a function. For example, Orange YES Brick NO x yx y -40 02 53 x y you cannot input a value that will force the function to take a square root of a negative or divide by zero. Asymptote x y 16 23 32 61 -6 -2-3 -2 -6

9. DOMAIN: The set of all possible x values that can be inputted into a function RANGE: The set of all possible y values that are outputted from a function. x greater than 5 x less than or equal to 10 y is between 0 and 100 z is at most 50 INTERVAL NOTATIONSET BUILDER NOTATION x is 5, 6 or 7

10. (4,4) (-5,-2) Ex. 2 Determine the domain and range (0,0) D: _________ R: _________ D: _________ R: _________

11. Domain and Range Challenge

12. 1. Find the Domain and Range D: ___________ R: ___________ [-6,5] [1,6]

13. 2. Find the Domain and Range Domain: ___________ Range: ___________ [-8,6[ ]-4,5]

14. 3. Find the Domain and Range Domain: ___________ Range: __________ ]-∞, ∞[ [-1, ∞[

15. 4. Find the Domain and Range D: ___________ R: ___________ [-1, ∞[ ] -∞, ∞[

16. 5. Find the Domain and Range D: ___________ R: ___________ ]-6, 6[ ] -5, 5[

17. 6. Find the Domain and Range D: _______________ R: ___________ [-∞, 0[ U ]0, ∞[ ] 0, ∞[

18. 7. Find the Domain and Range D: ___________ R: ___________ {1,3,5} {4,5,6}

19. Homework World 2-1 Homework