1. 1.6: Functions as Rules and Tables
Do NOW
1) Fill in the box in stage 0 and stage 4
2) What is the rule?
3) What is in the 63th stage?
4) Which stage has 37 blocks?
5) What is the similarities and differences between discrete and continuous?
Stage 0
Stage 1
Stage 2
Stage 3
2/27/ :29 AM
1.6: Functions as Rules and Tables

2. 1.6: Functions as Rules and Tables
Worksheet Key
2/27/ :29 AM
1.6: Functions as Rules and Tables

3. Relations and Functions
Section 1.6
©2012,
2/27/ :29 AM
1.6: Functions as Rules and Tables

4. 1.6: Functions as Rules and Tables
Definitions
Relation is a pairing of 2 items (like (x, y))
Domain is the X -values in a relation. Also known as INDEPENDENT Variable
Range is the Y -values in a relation. Also known as DEPENDENT Variable
“Y depends on X.”
Function is a relation that for each domain element, there is only 1 range element. _X_ do not repeat.
2/27/ :29 AM
1.6: Functions as Rules and Tables

5. x y D R I Think of: “A doctor needs his or her ID to eXamine you”
1.6: Functions as Rules and Tables

6. Example 1
The cost of a tank of gas depends on the number of gallons purchased. What is the input and output?
Input: Number of Gallons
Output: Cost of a tankful of gas
2/27/ :29 AM
1.6: Functions as Rules and Tables

7. Output: Volume of a Cube 1.6: Functions as Rules and Tables
Your Turn
The volume of a cube depends on the length of its edges. What is the input and output?
Input: Edge Length
Output: Volume of a Cube
2/27/ :29 AM
1.6: Functions as Rules and Tables

8. 1.6: Functions as Rules and Tables
Example 2
Identify the domain and range of this function:
2/27/ :29 AM
1.6: Functions as Rules and Tables

9. 1.6: Functions as Rules and Tables
Example 3
Identify the domain and range of this function: 4 –5 9 –1
Input –2 7
Output
2/27/ :29 AM
1.6: Functions as Rules and Tables

10. 1.6: Functions as Rules and Tables
Your Turn
Identify the domain and range of this function: 5 10 2 3 4
2/27/ :29 AM
1.6: Functions as Rules and Tables

11. Is a relation a function?
What is a function?
Can a function be a relation?
Can a relation be a function?
2/27/ :29 AM
1.6: Functions as Rules and Tables 11

12. 1.6: Functions as Rules and Tables
Example 4
Is this relation a function?
2/27/ :29 AM
1.6: Functions as Rules and Tables

13. 1.6: Functions as Rules and Tables
Your Turn
Is this relation a function?
2/27/ :29 AM
1.6: Functions as Rules and Tables

14. 1.6: Functions as Rules and Tables
Boys vs. Girls
Is this relation a function? a b c 1 2 3
Girls
Boys a b c 1 2 3
Girls
Boys
2/27/ :29 AM
1.6: Functions as Rules and Tables

15. 1.6: Functions as Rules and Tables
Example 5
Is this mapping a function?
Input
Output 1 2 4 8 6 12
2/27/ :29 AM
1.6: Functions as Rules and Tables

16. 1.6: Functions as Rules and Tables
Example 6
Is this mapping a function? 2 –1 3 –2
2/27/ :29 AM
1.6: Functions as Rules and Tables

17. 1.6: Functions as Rules and Tables
Your Turn
Is this mapping a function? 5 10 2 3 4
2/27/ :29 AM
1.6: Functions as Rules and Tables

18. 1.6: Functions as Rules and Tables
Making a Table
Establish the CONSTANT difference between the x and the y-coordinates
Plug in of what is given to us
2/27/ :29 AM
1.6: Functions as Rules and Tables

19. 1.6: Functions as Rules and Tables
Example 7
The domain of the function, y = 2x is 0, 2, 5, 7, and 8. Make a table and identify the range of the function. x
y = 2x 2 5 7 8 1 4 10 14 16 1 4 1
2/27/ :29 AM
1.6: Functions as Rules and Tables

20. 1.6: Functions as Rules and Tables
Example 8
The range of the function, y = x + 4 is 4, 6, 7, 10, and 11. Make a table and identify the domain of the function. x 2 3 6 7
y = x + 4 4 10 11
2/27/ :29 AM
1.6: Functions as Rules and Tables

21. 1.6: Functions as Rules and Tables
Example 9
Write the rule of this function: x y 2 1 3 4 6 8 10 12
2/27/ :29 AM
1.6: Functions as Rules and Tables

22. 1.6: Functions as Rules and Tables
Your Turn
Write the rule of this function: x y 1 2 4 3 7 6 9 8
2/27/ :29 AM
1.6: Functions as Rules and Tables

23. 1.6: Functions as Rules and Tables
Assignment
Pg 38:
4-20 even
2/27/ :29 AM
1.6: Functions as Rules and Tables