Today’s Lesson:

1. Today’s Lesson: What: Identifying a function Why: To identify a function and become familiar with basic function vocabulary. Input Output

2. Coordinate plane review: y Q I Q II C E A B D F G origin x Q III Q IV

3. Essential vocabulary: Ordered Pair A name we use for the x and _______ values that make up a point on the coordinate plane. y Relation A group of ordered _____________________. pairs Function A special ___________________ of relation where there is one and only one “y” value for every “x” value. (“x” can never repeat) TYPE All functions are relations, but Not all relations are functions!!!

4. 3 ways to name “X” and “Y”: OUTPUT DOMAIN DEPENDENT What is the Domain of the following relation? {(1,2); (2,3); (3, 4); (4,5)} _____________________________________ D = {1, 2, 3, 4} What is the Range of the following relation? {(1,3); (2,5); (3, 7); (4,9)} ______________________________________ R = {3, 5, 7, 9}

5. 4 ways to represent a function: As an equation y = _______ 4x - 2 With ___________ “y is equal to the product of 4 and x, minus two.” WORDS As a table Recognize this pattern/ equation? 4 2 3 1 10 As a _________ GRAPH

6. How to identify a function . . . METHOD ONE: Look to see if the “x” values repeat . . . If there is more than one _______ value that is the same #, then the relation is ___________ a function! x NOT Are the following examples functions? Answer “YES” or “NO” ___________ 2) _____________ 3) ______________ YES YES NO 4) __________ { (-2, 0); (0, 2); (2, 0); (4, 6) } YES 5) __________ { (-2, 0); (0, 3); (-2, 2 ); (5, 7) } NO

7. METHOD TWO: VERTICAL LINE TEST—Look at the graph of the function. If any two points on the graph can be connected by a ________________ line, then the relation is NOT a function! vertical Are the following examples functions? Answer “YES” or “NO” NO YES __________ 2) __________ 3) __________ 4) __________ YES NO

8. END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day.

9. NAME: DATE: ______/_______/_______ Math-7 NOTES What: identifying a function Why: To identify a function and become familiar with basic function vocabulary. Coordinate plane review: Essential vocabulary: Ordered Pair A name we use for the x and _____ values that make up a point on the coordinate plane. Relation A group of ordered __________________. Function A special _______________ of relation where there is one and only one “y” value for every “x” value. (“x” can never repeat) All functions are relations, but Not all relations are functions!!!

10. 3 ways to name “X” and “Y”: What is the Domain of the following relation? {(1,2); (2,3); (3, 4); (4,5)} _________________________________ What is the Range of the following relation? {(1,3); (2,5); (3, 7); (4,9)} _________________________________ 4 ways to represent a function: As an equation y = _______ “y is equal to the product of 4 and x, minus two.” With ___________ 4 2 3 1 Recognize this equation?? As a table As a _______

11. How to identify a function . . . METHOD ONE: Look to see if the “x” values repeat . . . If there is more than one _______ value that is the same #, then the relation is ______ a function! Are the following examples functions? Answer “YES” or “NO” ____________ 2) _______________ 3) _______________ 4) __________ { (-2, 0); (0, 2); (2, 0); (4, 6) } 5) __________ { (-2, 0); (0, 3); (-2, 2 ); (5, 7) } METHOD TWO: VERTICAL LINE TEST—Look at the graph of the function. If any two points on the graph can be connected by a ________________ line, then the relation is NOT a function! Are the following examples functions? Answer “YES” or “NO” 1) __________ 2) __________ 3) __________ 4) __________

12. NAME:_________________________________________________________________________________ DATE:_____/_____/__________ Math-7 PRACTICE/ classwork “ function vocabulary” A __________________________________ is a group of ordered pairs. A ________________________________ is a special type of relation where all the “x” values match with one and only one “y” value. (the “x” can never repeat). We have 3 ways to name both the “x” variable and the “y” variable. Fill in the missing information with the appropriate vocabulary: What is the Domain of the following relation? {(0,3); (-5,5); (-2, 7); (8,9)} D = _________________________________ What is the Range of the following relation? {(1,-2); (2,0); (3, 2); (4,4)} R= _________________________________ 6) What are the 4 ways to represent a function (from our notes)?

13. NAME:_________________________________________________________________________________ DATE:_____/_____/__________ Math-7 PRACTICE/ Homework “ Is it a function??”

14. NAME:_________________________________________________________________________________ DATE:_____/_____/__________ Math-7 PRACTICE/ Homework “ Identify a function from a graph”