1. Relations and Functions

2.  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.

3.  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).

4.  Each value of domain matches to one AND ONLY ONE value in the range. DomainRange 234234 -3 5 6

5. Domain Range 148148 0 2 -5 Since a value in the domain goes to more than one value in the range, this is NOT a relation

7.  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.

9.  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.

13.  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

20.  Worksheet 2-1