2.1 Relations and Functions
Real Numbers are ordered by use of a number line.
Ordered pairs are organized by points in a plane
called the rectangular coordinate system, or the
Cartesian plane (1596-1650 Rene Descartes).
Rectangular Coordinate System
The following is the rectangular coordinate system:
It is made up of two number lines:
The horizontal number line is the x- axis.
The vertical number line is the y- axis.
The origin (0,0) is where the two intersect. This is where both number
lines are 0. The two number lines split the plane into four
quadrants which are marked on this graph with Roman numerals.
Each point on the graph is associated with an ordered pair. When
dealing with an x, y graph, 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).
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).
Let A= {a,b,c} B={1,2,3,4,5}
Function?
Yes
Function?
Function?
No
No
Function- correspondence between every element in the
domain (x) to exactly one element in the range (y).
Discrete function- a set of individual points (not connected).
Function?
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.
Function?
Function?
Yes
Yes
Function?
Function?
No
No
Continuous function- infinitely many points (connected).
Determine whether each of the following equations represents a
function.
1) y  3 x  4
2) x  y  1
2
Functional Notation:
y  3x  4
Can be written…..
f x  3x  4
Read f of x.
f is the name of the function
g x, hx, px, as well as any other letter of the alphabet may also be used to represent the function.
Suppose : f x  2x  4.
Find : f (6)  26  4  8
Graphical representation of what just happened:
8
When x =6
y =8
6
Given the function :
d ( x)  x 2  8
Find : d  2  
Find : d 7a  
Given : f x   .5 x 2  4 x  2.5
Use your graphing calculator to
find :
f 4.6 
Given the function :
x 2  3x  2
h x  
x2
Find :
ha 1 