Guided Notes: Functions and Relations Vocabulary A relation can be represented by a set of _______________________________ The domain is the set of all ______________________________ The range is the set of all __________________________ The independent variable is the same as the ___-values and the ___________________ The dependent variable is the same as the ___-values and the ___________________ A relation is a function if for each ___-value there is exactly ______ ___-value. Each value in the domain of a function is called an _____________________, and the corresponding value for the range is called an _______________________. Examples: Identify the domain and range of each relation. 1. {(-2, 0), (0, 3), (4, -7), (-2, -1) 2. Domain: Range: x -4 -1 2 3 y 1 -5 8 1 Domain: Range: Examples: Determine whether the relation is a function. Explain why or why not. 3. {(-5, 0), (0, 1), (0, 4), (3, -7)} 4. x 2 6 1 -1 y 1 3 8 3 5. x -1 0 3 3 y -2 -3 0 1 When given a graph or picture of a relation and asked if it is a function the ______________ __________ ___________ is used. This test helps you to know a relation is a function by looking to see if any ___________ line drawn does not intersect the graph at more than one point. In other words on the graph each ___-value is paired with only one ___-value. Examples: Determine if the graphs below represent functions or not by using the Vertical Line Test. y 6. 5 -- . . . . . 7. 5 x 5 -- y 8. .. . . . x 5 9. Mapping diagrams and tables can be used to determine if a relation is a function. In a mapping diagram or table each ___-value will be paired with only one ___-value. (A y-value may be paired with more than one x-value and the relation will still be a function.) Examples: Determine whether the mapping diagram or table represents a function and circle yes or no. 10. function: yes or no 13. function: yes or no input output 1 -4 3 0 -2 3 5 6 x y -6 1 3 8 2 7 11. function: yes or no 14. function: yes or no x y -1 -2 3 4 8 5 12. function: yes or no input output -4 -1 -1 2 0 7 5 15. function: yes or no x y 1 3 -2 -4 9 3 4 2 -5 3 input output -2 3 4 5 3 8 -2 4 It is a one to one function when every element of the range of the function corresponds to exactly ______ element of the domain. y = f(x) is a function if it passes the __________ _____ ________. It is a 1-1 function if it passes both the _________ ______ __________ and the _____________ ______ __________ . Examples: Determine whether the representations are one to one functions. 16. 17. 18. x y 1-1: 1-1: 1-1: 1 5 Yes or No Yes or No Yes or No 2 8 3 11 4 14 19. x y 20. 21. 1-1: 1 3 1-1: 1-1: -2 -4 Yes or No Yes or No 3 4 -5 3 Yes or No 22. Make a set of ordered pairs that represents a one to one function: