1. FUNCTIONS Relation – a set of ( x, y ) points Function – a set of ( x, y ) points where there is only one output for each specific input – x can not be paired with more than one y ** just make sure x doesn’t repeat itself Ways to represent functions : 1. A set of ( x, y ) coordinates 2. A mapping 3. An equation

2. FUNCTIONS Relation – a set of ( x, y ) points Function – a set of ( x, y ) points where there is only one output for each specific input – x can not be paired with more than one y ** just make sure x doesn’t repeat itself Ways to represent functions : 1. A set of ( x, y ) coordinates 2. A mapping 3. An equation The DOMAIN of a function are its x values, its RANGE are the y values

3. This relation represents a true function, notice that the x coordinate never repeats… ( 1, 3 ), ( 2, 4 ), ( - 5, - 3 ), ( 0, 2 )

4. This relation represents a true function, notice that the x coordinate never repeats… ( 1, 3 ), ( 2, 4 ), ( - 5, - 3 ), ( 0, 2 ) Lets look at a mapping. Mapping has the x’s on one side and the y’s on the other side. You draw arrows showing which x is associated with which y.

5. This relation represents a true function, notice that the x coordinate never repeats… ( 1, 3 ), ( 2, 4 ), ( - 5, - 3 ), ( 0, 2 ) Lets look at a mapping. Mapping has the x’s on one side and the y’s on the other side. You draw arrows showing which x is associated with which y. Let’s use the ( x, y ) pairs from the above example: x y 1 2 -5 0 2 - 3 4 3

6. This relation represents a true function, notice that the x coordinate never repeats… ( 1, 3 ), ( 2, 4 ), ( - 5, - 3 ), ( 0, 2 ) Lets look at a mapping. Mapping has the x’s on one side and the y’s on the other side. You draw arrows showing which x is associated with which y. Let’s use the ( x, y ) pairs from the above example: x y 1 2 -5 0 2 - 3 4 3

7. This relation represents a true function, notice that the x coordinate never repeats… ( 1, 3 ), ( 2, 4 ), ( - 5, - 3 ), ( 0, 2 ) Lets look at a mapping. Mapping has the x’s on one side and the y’s on the other side. You draw arrows showing which x is associated with which y. Let’s use the ( x, y ) pairs from the above example: x y 1 2 -5 0 2 - 3 4 3

8. This relation represents a true function, notice that the x coordinate never repeats… ( 1, 3 ), ( 2, 4 ), ( - 5, - 3 ), ( 0, 2 ) Lets look at a mapping. Mapping has the x’s on one side and the y’s on the other side. You draw arrows showing which x is associated with each y. Let’s use the ( x, y ) pairs from the above example: x y 1 2 -5 0 2 - 3 4 3

9. xy 1 2 -2 1 4 Does the mapping show a true function ?

10. xy 1 2 -2 1 4 Does the mapping show a true function ? YES !!! Each x has only one y in the mapping ** its acceptable for y to have more than one match

11. xy 2 -2 1 -3 4 Does the mapping show a true function ?

12. xy 2 -2 1 -3 4 Does the mapping show a true function ? NO !!! Notice that 2 has two matches.

13. xy 2 -2 1 -3 4 Does the mapping show a true function ? NO !!! Notice that 2 has two matches. If we showed the mapping as coordinates, you see that x repeats. ( 2, 1 ), ( 2, 4 ), ( - 2, - 3 )

14. FUNCTIONS : There is a special notation to show a function.

15. FUNCTIONS : There is a special notation to show a function. - Read “f of x “ - There is a function f that has x as its variable - it’s a different way of saying ”y” - coordinate is ( x, f(x) )

16. FUNCTIONS : There is a special notation to show a function. The rule of the function

17. FUNCTIONS : There is a special notation to show a function. We can generate some ( x, f(x) ) points by picking some values for x, plugging them into the rule and solving for f(x)

18. FUNCTIONS : There is a special notation to show a function. We can generate some ( x, f(x) ) points by picking some values for x, plugging them into the rule and solving for f(x) When substituting a value for x, you show it in the f(x) notation…lets use x = 1 x f(x)

19. FUNCTIONS : There is a special notation to show a function. We can generate some ( x, f(x) ) points by picking some values for x, plugging them into the rule and solving for f(x) When substituting a value for x, you show it in the f(x) notation…lets use x = 1 x f(x) 18

20. FUNCTIONS : There is a special notation to show a function. We can generate some ( x, f(x) ) points by picking some values for x, plugging them into the rule and solving for f(x) When substituting a value for x, you show it in the f(x) notation…lets use x = 2 x f(x) 18 2 11

21. FUNCTIONS : There is a special notation to show a function. We can generate some ( x, f(x) ) points by picking some values for x, plugging them into the rule and solving for f(x) When substituting a value for x, you show it in the f(x) notation…lets use x = 3 x f(x) 18 2 11 3 14

22. FUNCTIONS : There is a special notation to show a function. We can generate some ( x, f(x) ) points by picking some values for x, plugging them into the rule and solving for f(x) You could keep going here, 3 points is enough for a linear function. x f(x) 18 2 11 314

23. FUNCTIONS : There is a special notation to show a function. We can generate some ( x, f(x) ) points by picking some values for x, plugging them into the rule and solving for f(x) Does this set of points satisfy a true function ? x f(x) 18 2 11 314

24. FUNCTIONS : There is a special notation to show a function. We can generate some ( x, f(x) ) points by picking some values for x, plugging them into the rule and solving for f(x) Does this set of points satisfy a true function ? YES… x f(x) 18 2 11 314

25. FUNCTIONS : When generating points for quadratics, cubics, etc, it is a good idea to get 5 – 8 points ( + / - ) to show your relation and to eventually graph your function… Below is the work to generate the ( x, f(x) ) coordinates for the given function… x f(x) -2 0 1 2 -10 -3 -2 6

26. FUNCTIONS : When evaluating functions, sometimes algebraic expressions are used… Complete the table below…

27. FUNCTIONS : When evaluating functions, sometimes algebraic expressions are used… Complete the table below… 4

28. FUNCTIONS : When evaluating functions, sometimes algebraic expressions are used… Complete the table below… 412

29. FUNCTIONS : When evaluating functions, sometimes algebraic expressions are used… Complete the table below… 412 a

30. FUNCTIONS : When evaluating functions, sometimes algebraic expressions are used… Complete the table below… 412 aa 2 – 4

31. FUNCTIONS : When evaluating functions, sometimes algebraic expressions are used… Complete the table below… 412 aa 2 – 4

32. FUNCTIONS : When evaluating functions, sometimes algebraic expressions are used… Complete the table below… 412 aa 2 – 4

33. FUNCTIONS : When evaluating functions, sometimes algebraic expressions are used… Complete the table below… 412 aa 2 – 4 2x + h