Relations and Functions

Rectangular Coordinate System

Goal: Briefly discuss the definition of functions, and domain and range.

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).

The following is the rectangular coordinate system:

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- correspondence between every elementin one set (x) to exactly one element in another set (y).

Function? Yes

Let A= {a,b,c} B={1,2,3,4,5}

Function? Yes Function? No

Function- correspondence between every element in the domain (x) to exactly one element in the range (y).

Function? No

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

Yes

Discrete function- a set of individual points (not connected).

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.

Function?

Function? Yes Function? No

Function? Yes Function? No

Determine whether each of the following equations represents a function by graphing these equations on your graphing calculator.

43)1 xy

1)2 2 xy

Continuous function- infinitely many points (connected).

Functional Notation:

43 xy Can be written…..

43 xxfRead f of x.

function. therepresent toused be alsomay alphabet theofletter other any as wellas,,, xpxhxg

f is the name of the function

.42 :Suppose xxf

)6( :Find f 462

Graphical representation of what just happened:

6

8

8

When x =6 y =8

2:

8)(

:function Given the2

dFind

xxd

adFind 7:

6.4

:find

tocalculator graphingyour Use

5.245.: 2

f

xxxfGiven