1. Warm-Up
Graph the point (2, -3)
If 𝑦=3𝑥−7 and 𝑥=10, solve for y.

2. Relations and Functions
Objective:
To graph a relation, state the domain and range, and determine if it is a function.
To find values of functions for given elements of the domain.

3. Relations and Ordered Pairs
Relation: is a set of ordered pairs.
Ordered Pair: Points in a plane that can be located by using ordered pairs of real numbers. An ordered pair consists of the coordinates of the point.
Example: (3, 7) 3 is the x-coordinate, 7 is the y- coordinate.

4. Coordinate Plane
Cartesian Coordinate Plane: Composed of the x-axis and the y-axis which meet at the origin and is divided into four quadrant.
x-axis: The horizontal number line on the coordinate plane.
y-axis: The vertical number line on the coordinate plane.
Origin: The point (0, 0) at which the axes of the coordinate plane intersect.

5. Cartesian Coordinate Plane

6. Domain and Range
Domain: all if the x-values from the ordered pairs from the relation.
Range: all if the y-values from the ordered pairs from the relation.
Example:
Relation: {(4,5), (6, -2), (8, 1)}
Domain: {4, 6, 8}
Range: {-2, 1, 5}

7. Functions
A function is a special type of relation in which each element of the domain is paired with exactly one element of the range. Mapping: shows how each member of the domain is paired with each member of the range. Vertical Line Test: If every vertical line drawn on a graph of a relation passes through no more than one point of the graph, then the relation is a function.

8. Vertical Line Test

9. Continuous vs Discrete
Discrete Function: A functions whose graph consists of points that are not connected.
Continuous Function: is graphed with a line or smooth curve and has a domain with an infinite number of elements.

10. Homework
Practice 2-1 “Relations and Functions”