1. Relations and Functions
Section 2.1
©2012,
4/17/2019 7:07 PM
2.1: Relations and Functions

2. 2.1: Relations and Functions
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.
4/17/2019 7:07 PM
2.1: Relations and Functions

3. x y D R I Think of: “A doctor needs his or her ID to eXamine you”
4/17/2019 7:07 PM
2.1: Relations and Functions

4. 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
4/17/2019 7:07 PM
2.1: Relations and Functions

5. Output: Volume of a Cube 2.1: Relations and Functions
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
4/17/2019 7:07 PM
2.1: Relations and Functions

6. 2.1: Relations and Functions
Example 2
Identify the domain and range of this function:
4/17/2019 7:07 PM
2.1: Relations and Functions

7. 2.1: Relations and Functions
Example 3
Identify the domain and range of this function: 4 –5 9 –1
Input –2 7
Output
4/17/2019 7:07 PM
2.1: Relations and Functions

8. 2.1: Relations and Functions
Your Turn
Identify the domain and range of this function:
4/17/2019 7:07 PM
2.1: Relations and Functions

9. Is a relation a function?
What is a function?
Can a function be a relation?
Can a relation be a function?
4/17/2019 7:07 PM
2.1: Relations and Functions 9

10. 2.1: Relations and Functions
Example 4
Is this relation a function?
4/17/2019 7:07 PM
2.1: Relations and Functions

11. 2.1: Relations and Functions
Your Turn
Is this relation a function?
4/17/2019 7:07 PM
2.1: Relations and Functions

12. 2.1: Relations and Functions
Boys vs. Girls
Is this relation a function? a b c 1 2 3
Girls
Boys a b c 1 2 3
Girls
Boys
4/17/2019 7:07 PM
2.1: Relations and Functions

13. 2.1: Relations and Functions
Example 5
Which mapping is a function?
Choice A: Choice B: 3 1 –1 2 2 –1 3 –2
4/17/2019 7:07 PM
2.1: Relations and Functions

14. 2.1: Relations and Functions
Your Turn
Which mapping is a function?
Choice A: Choice B:
4/17/2019 7:07 PM
2.1: Relations and Functions

15. 2.1: Relations and Functions
Vertical Line Test
Vertical Line Test: a relation is a function if a vertical line drawn through its graph, passes through only one point. AKA: “The Pencil Test” Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function
4/17/2019 7:07 PM
2.1: Relations and Functions

16. 2.1: Relations and Functions
Example 6
Would this graph be a function?
4/17/2019 7:07 PM
2.1: Relations and Functions

17. 2.1: Relations and Functions
Example 7
Would this graph be a function?
4/17/2019 7:07 PM
2.1: Relations and Functions

18. 2.1: Relations and Functions
Your Turn
Would this graph be a function?
4/17/2019 7:07 PM
2.1: Relations and Functions

19. 2.1: Relations and Functions
Evaluating Functions
Replace its variable with a given number or expression.
Remember to think of the function machine; for every x, there is a y-coordinate
4/17/2019 7:07 PM
2.1: Relations and Functions

20. 2.1: Relations and Functions
Example 8
Given g(x) = x2 – 3, determine g(2).
(2)2
g(2) = 4 – 3
g(2) = 1
4/17/2019 7:07 PM
2.1: Relations and Functions

21. 2.1: Relations and Functions
Example 9
Given f(x) = x2 – 2x + 4, evaluate f(–5).
4/17/2019 7:07 PM
2.1: Relations and Functions

22. 2.1: Relations and Functions
Your Turn
Given f(x) = x2 – 6x + 9, evaluate f(1/2).
4/17/2019 7:07 PM
2.1: Relations and Functions

23. 2.1: Relations and Functions
Assignment
Page 76
3-23 odd, odd
4/17/2019 7:07 PM
2.1: Relations and Functions