1. Rectangular Coordinate System
Relations and Functions
Goal: Briefly discuss the definition of functions, and domain and range.
Rectangular Coordinate System

2. The following is the rectangular coordinate system:
The x coordinate is always first and the y coordinate is always second in the ordered pair (x, y).  It is a solution to an equation in two variables.  Even though there are two values in the ordered pair, be careful that it associates to ONLY ONE point on the graph,  the point lines up with both the x value of the ordered pair (x-axis) and the y value of the ordered pair (y-axis).

3. Relation- a set of ordered pairs. i.e. {(2,4) (1,-2) (5,6)}
Domain- the set of all “x” or first coordinates from the ordered pair.
Range- the set of all “y” or second coordinates from the ordered pair.
Mapping
Q.B.’s
T.D. Passes
Function?
Yes
Function- correspondence between every element
in one set (x) to exactly one element in another set (y).

4. Let A= {a,b,c} B={1,2,3,4,5}
Function?
Yes
Function? No
Function? No
Function- correspondence between every element in the domain (x) to exactly one element in the range (y).

5. *Make sure to write domain and range in ascending order!

6. Discrete function- a set of individual points (not connected).
Yes
Vertical Line Test- If a vertical line crosses a graph at only one point it is a function. If the vertical line crosses the graph more than once it is not a function.

7. Function?
Yes
Function? No
Function?
Yes
Function? No

8. Continuous function- infinitely many points (connected).
Determine whether each of the following equations represents a function by graphing these equations on your graphing calculator.

9. Functional Notation:
Can be written…..
Read f of x.
f is the name of the function

10. Graphical representation of what just happened:8
When x =6
y =8 6