1. Unit 3 Day 4

2. Warm-Up 2 Write the Now/Next Function Rule for 3, -9, 27, -81, …
Write the Input/Output Function Rule for the table to the right:
What is a difference between recursive functions and explicit functions>
Input -1 -3 4 6
Output 1 3 -4

3. HW Check f(x) = x-5 2. f(x) = x/3 3. f(x) = -4x 4. f(x) = 2x+1

4. A RELATION is a set of ordered pairs (input/output values)

5. DOMAIN
The DOMAIN of a relation is the set of first coordinates of the ordered pairs. ***The X values are the DOMAIN*** ***Input Values***

6. RANGE
The RANGE is the set of second coordinates. ***The Y values are the RANGE*** ***Output Values***

7. Function
A FUNCTION is a relation that assigns exactly one value in the range to each value in the domain. ***Meaning X values CANNOT Repeat***

8. a) Domain: _______________________ b) Range: _________________________ c) Is the relation a function? Why or Why not. X Y 4 3 -2 1 -1

9. EXAMPLE Tell whether each table represents a function
EXAMPLE Tell whether each table represents a function. Explain why or why not.
-- In your packet!

10. Domain Values Range Values Domain values “map” to its matching range value

11. Create a Mapping Diagram for the relation Is the relation a function
Create a Mapping Diagram for the relation Is the relation a function? Why or Why not.

13. Recall: Function
A function is a relation from one set (called the__________) to another set (called the ___________) that assigns to each input value exactly ________ output value.

14. Relations can be represented in 4 different ways
Table
Equation
Graph
Mapping Diagram

17. If given a graph of a relation and asked to determine if the relation is a function: Use the VERTICAL LINE TEST
If any vertical line passes through more than one point of the graph, the relation is not a function.

18. Is the relation a Function?

23. (city, zip code) b. (person, birth date)
EXAMPLE Does each relationship of the form (input, output) represent a function? If the relationship does not represent a function, find an example of one input that has two or more outputs.
(city, zip code) b. (person, birth date)
c. (last name, first name) d. (state, capital)
2. Give an example of an (input, output) relationship that is a function.
3. Give an example of an (input, output) relationship that is not a function.

24. EXAMPLE Determine whether each table of x- and y-values represents a function. Explain your reasoning.

25. HW 3.4