Transcript Lesson 2.1 Notes - Math with Mr. Gillam

Lesson 2.1 (Day 1) Notes
Functions and Their Graphs
Relations
What is a relation?
A relation is a set of ordered pairs (x,y).
Example: {(1,2), (2,3), (3,4), (4,5)}
All problems covered in this chapter will be relations.
How can a relation be represented?
A relation may also be represented as a table.
Input
Output
Domain
The inputs of a relation.
Input
Output
Domain
They may also be represented by the x values in a
set of ordered pairs.
{(1,5), (2,6), (3,7), (4,8)}
{(2,4), (7,9), (12,20)}
{(1,2), (3,4), (5,6)}
Range
The outputs of a relation.
Input
Output
Range
They may also be represented by the y values in a set of
ordered pairs.
{(1,5), (2,6), (3,7), (4,8)}
{(2,4), (7,9), (12,20)}
{(1,2), (3,4), (5,6)}
Functions
For each x value there is exactly one y value.
For each domain, there is exactly one range.
Functions
Are these relations functions?
{(1,2), (2,3), (2,5)}
{(2,3), (1,2), (3,4)}
Functions
Input
Output
Vertical Line Test
The vertical line test is a way to decide if a relation
is a function, when examining the graph of the
relation.
To use the vertical line test you must:
•Plot each point.
•Align your pencil vertically on the left side of your
paper.
•Slide your pencil across your paper
•To pass the test, there can never be two points
touching your pencil at the same time
•If there is any time where your pencil crosses two
points while it is still vertical, the relation cannot be a
function
•If there is only one point at any time on the pencil
after sliding it across the paper, then it passes the test
and the relation is a function
Homework
 Page 70 14-26