Transcript Chapter 2 Lesson 1

Relations and Functions
 Ordered Pair- A pair of coordinates, written in the form
(x,y), used to locate any point on a coordinate plane.
 Cartesian Coordinate Plane- Plane composed of x-axis and
y-axis which meet at the origin (0,0) and divide the plane
into 4 quadrants.
 Quadrants- The 4 areas of the Cartesian Coordinate Plane.
 Relation- Any set of ordered pairs, graph on a line, table of
values, or picture representation of domain and range.
 Domain- The set of all x-coordinates from the ordered
pairs of a relation.
 Range- The set of all y-coordinates from the ordered pairs
of a relation.
 Function- Special type of relation in which each element
of the domain is paired with EXACTLY ONE element of the
range.
 Mapping- Shows how members of a function are paired.
 One-to-One Function- Each element of the range is paired
with exactly one element of the domain.
 Discrete Function- A relation in which the domain is a set
of individual points.
 Continuous Function- The domain of the relation has a
infinite number of elements and the relation can be
graphed with a line or smooth curve.
 Vertical Line Test- Test used to determine whether a graph
is a function or not.
 Independent Variable- Values that make up the domain.
 Dependent Variable- Values that make up the range.
 Function Notation- An equation of y in terms of x, written
as y=f(x).
 Each value of domain matches to
one AND ONLY ONE value in the
range.
Domain
Range
2
-3
3
5
4
6
Domain
Range
1
0
4
2
8
-5
Since a value in the domain goes to more than one value in the range, this is NOT a relation
When given a set of ordered
pairs:
 A function has a set of ordered pairs
where none of the x-values (first
number in the ordered pair) are the
same in more than one ordered pair.
 When an x-value is repeated in more
than one ordered pair, the relation is
not a function.
 If data is given in table form, rewrite
values as ordered pairs.
 When given a graph representation, use the
vertical line test to determine whether a
relation is a function.
 A graph of a function will intersect a vertical line in only
one place, regardless of where the vertical line is drawn.
 A graph of a non-function will intersect a single vertical
line two or more times.
 Discrete- A finite number of
ordered pairs surrounded by { }
 Discrete Graph- not continuous
line, only shows points on the
graph
 Domain and Range are finite numbers
 Continuous- a function of the form
y=mx+b
 Continuous Graph- shows line with
arrows on both sides
 Domain is all real numbers, Range is
either finite or all real numbers
Worksheet 2-1