1. 1.6 Relations and Functions

2. Appetizers . . . Can a student have more than one telephone number?
Can a student have more than one height?
Can a phone number belong to more than one person?

3. Some Vocabulary so we all speak the same language . . .
relation: a pairing of input values with output values, such as an ordered pair. For any (x, y), x is the input and y is the output.
domain: set of input values for a relation.
range: set of output values for a relation.

4. Table Graph Mapping Diagram 123456 9 13 15 12 10 Ordered Pairs
{(1, 9), (2, 13), (3, 15), (4, 15), (5, 12), (6, 10)}
domain (input)
range (output)

5. Function or not a function? That is the question!
function: there is only one output for each input, so each element of the domain is mapped to exactly one element in the range.
Huh? No repeats for x. Repeats on y are OK. A B C A B C 2 2
NOT a function
Function
{2, A), (2, B), (2, C)} 2 is used more than once
{A, 2), (B, 2), (C, 2)} 2 is used more than once

6. Function or not a function? That is the question!
Press Function or NOT a Function, then explain. -2 -1 1 2 5 6 7 8 X
Function
NOT a Function

7. Function or not a function? That is the question!
Press Function or NOT a Function, then explain. -2 -1 1 2 3 4 5 X
Function
NOT a Function

8. Function or not a function? That is the question!
Press Function or NOT a Function, then explain.
Input Value –2 –1 1 2
Output Value –8 8 X
Function
NOT a Function

9. Function or not a function? That is the question!
Press Function or NOT a Function, then explain.
Input Value 1 2
Output Value –4 –2 4 X
Function
NOT a Function

10. Function or not a function? That is the question!
Press Function or NOT a Function, then explain.
{(1, 0), (2, –1), (3, 0), (3, – 1), (4, 0)} X
Function
NOT a Function

11. Function or not a function? That is the question!
Press Function or NOT a Function, then explain.
{(1, 0), (2, –1), (3, 0), (4, –1)} X
Function
NOT a Function

12. What about graphs?
Vertical line test (VLT): If any vertical line passes through more than one point on the graph of a relation the relation is not a function.
Function

13. VLT, cont.
Not a Function

14. VLT, cont.
Function
Not a Function

15. VLT, cont.
Function
Not a Function

16. VLT, cont.
Function
Not a Function

17. VLT, cont.
Function
Not a Function

18. VLT, cont.
Function
Not a Function

19. VLT, cont.
Function
Not a Function

20. Finding Domain and Range from a Graph

21. Helicopter taking off, hovering briefly, then landing.

22. Speeding baseball being caught by an outfielder.

23. Helicopter taking off, hovering briefly, then landing.

24. 1.7 Function Notation

25. y is now f(x)
function
function notation
Find y when x=-3; or evaluate the function when x=-3

26. Any letter goes!
function
function notation