4.2. Relations and Functions Introduction College Algebra 4.2. Relations and Functions Introduction

Do Now: Determine the Domain and Range of the following two graphs

Homework? Questions? Comments? Confusions? ASK ASK ASK ASK!

Yesterday We looked at domain and range. Today? Let’s determine the domain and range and other aspects of relations!

Relation: Relation: A set of ordered pairs Ex: *Realize: Relations will always be discrete!

Relations (Continued) Relations can be expressed in four different ways: 1. A list of coordinate points 2. A Table 3. A Graph 4. A Mapping Diagram

Mapping Diagrams Mapping: A diagram that illustrates how each x coordinate is paired with a y coordinate. Example:

Realize With mapping diagrams All values are in number order- smallest to largest No values are repeated!

Example One: Express the relation {(1,1), (0,2), (3, -2)} as a table and a graph. What’s the domain and range of the relation? X Y

Example One (Continued) Create a mapping of {(1,1), (0,2), (3, -2)}

Example Two: Given the following mapping diagram, determine the graph, table, and list of coordinate points of the relation. What is the domain? Range?

Example Three: Given the graph of a relation, determine the mapping diagram, table, list of coordinate points, domain and range.

Example Four: Given the table, determine the mapping diagram, graph, list of coordinate points, domain and range of the relation.

You Try! For each of the given relations determine the missing pieces: Graph Mapping Diagram List of Coordinate points Table Domain Range

Graphs for You Try!

Do Now: Domain? Range? Create a LOCP

Functions Functions are a special type of relation– and the easiest way to discuss functions is to talk about soda machines!

Example Five: What is the problem with this machine? How could we fix it?

Example Six: Is this a good soda machine? Why/Why not?

Example Seven: Is this a good soda machine? Why/Why not?

Example Eight: Is this a good soda machine? Why/Why not?

Function A function is like a good soda machine. For every single input, there is exactly one output Input: Each x value Output: Each y value

Functions:

Example Nine: {(5,4), (6,3), (7,2)} Is the following relation an example of a function? {(5,4), (6,3), (7,2)}

Example Ten: Is the following relation an example of a function? {(5,4), (5,3), (5,2)}

You Try! Are the following relations functions?? {(3, -2), (8, 3), (-3, -3)} {(1, 0), (0, -2), (1, -2)}

Example Eleven: Is the relation below a function? Why or why not?

Example Twelve: Is the relation below a function or no? Why?

You Try! Are the following relations functions? Why or why not? X Y 2 3 4 5 -4 X Y 5 8 7 -2 6 12 1 -1

Example Thirteen: Function or no?

Example Fourteen: Function or no?

You Try! Function or no?

Example Fifteen (Real World!) Function or no? A machine in which you input an age and the machine gives you the name of any person who is that age. Pressing a letter on a keyboard and having that letter appear on the screen. A machine in which you input anyone’s name in the world and it will give you their date of birth.

Come up with your own! Come up with your own example of a relation machine. Then determine whether it is a function or not.

Practice Problems Try some on your own/in your table groups As always don’t hesitate to ask me questions if you are confused and/or ask your table mates. As we always know– they are your greatest resource!

Exit Ticket Create a mapping diagram and table for the following relation: {(0,0), (1,3), (4,2), (3, 1)} Does the following relation express a function? Why? Why not? {(5,1), (6,7), (8,1), (2, 3)}