1. Module 4, Lesson 1 Online Algebra VHS@PWCS
Intro To Functions
Module 4, Lesson 1
Online Algebra

2. This is an important skill that we will use a lot from hear on out.
Graphing review
If you cannot remember how to graph points on a coordinate plane from Pre-Algebra, then you can do one of 2 things or both!
Review page 58 in your textbook.
Look at the video title graphing review
This is an important skill that we will use a lot from hear on out.

3. Relations In algebra a relation is a set of ordered pairs.
They do not have to have a rule, but can be any set of ordered pairs.
Because we are talking about sets, we need to use braces { }. Braces mean all of these things are in a set.
An example of a relation is below:
{(3, 2), (0, 0), (4, 9), (-3, -7)}

4. Different Ways To Show Relations.
One of the ways to show the relation {(4, 5), (4, 2), (-1, -1), (2, -1)} is a mapping.
Each x- value MAPS to a y-value.
The arrows show us the ordered pairs.
Notice that x-coordinate of 4 has two y – values (2 and 5), but 4 is used once, but the two arrows indicate the different ordered pairs.
X – coordinates
Y – Coordinates -1 2 4 -1 2 5

5. Different Ways To Show Relations
Two other ways to show the relation {(4, 5), (4, 2), (-1, -1), (2, -1)} are a table and a graph.
(4, 5)
Graph:
Table: X Y -1 2 4 5
(4, 2)
(-1, -1)
(2, -1)

6. A relation is made up of domain and a range.
Domain and Range
A relation is made up of domain and a range.
The Domain is the set of all x-coordinates.
Other names for the domain are independent variables and input.
The Range is the set of all y-coordinates.
Other names for the range are dependent variables and output.

7. Domain and Range
What is the domain and range of the following relation?
Domain: {-1, 2, 4}
Notice that even though there are two fours, we only state it once. We also used braces because the domain is a set.
Range: {-1, 2, 5}
Notice that even though there are two negative ones, we only state it once. We also used braces because the range is a set. X Y -1 2 4 5

8. Relation Review A relation is a set of ordered pairs.
The can be displayed 4 different ways
Set of ordered pairs
Mapping
Table
Graph
A relation is made up of a domain and range.
The domain is all the x-coordinates
Other names for the domain are: independent variables and input
The range is all the y-coordinates.
Other names for the range are: dependent variables and output.

9. Functions A function is a special relation.
A function assigns exactly one value of the dependent variable to each value of the independent variable.
In other words each x – coordinate maps to only 1 y-coordinate.

10. How To Tell if a Relation is a Function.
In a table or set of ordered pairs, if an x-value repeats then it is not a function. X Y -1 2 4 5 X Y -1 2 6 -5 10
Notice the 4 repeats, so it is not a function!
In this relation, no x-values repeat, so this is a function.
It is okay for y-values to repeat.

11. How To Tell if a Relation is a Function.
In a mapping each x, should have only 1 arrow coming from it. X 2 4 Y -2 -1 X 2 4 6 Y -2 -1
This is a function
This is not a function

12. Different Ways To Show Relations
In a graph, we use a vertical line test. If the graph passes through the vertical line more than once it is not a function.
The vertical line goes through the graph at 2 places it is not a function.
Here no matter where we draw a vertical line, that line will only go through our graph once. So this is a function.

13. Which of the following are functions?
{(0, 2), (1, 2) (3, 2)} x 1 3 y -2 4
Only the set of ordered pairs is a function, in both the table and the mapping there is an x that repeats and the graph fails the vertical line test. x 3 4 Y -1 3

14. Function Review
Remember that a function is a special relation where each member of the domain maps to exactly one member of the range.
Other names for the domain are: x-coordinates, input, independent variable
Other names for the range are: y-coordinates, output, dependent variable.