1. 2-1 Relations and Functions Objective: To graph a relation, state its domain and range, and determine if it is a function, and to find values of functions for given elements in a domain.

2. Drill #16* Evaluate the

3. Drills and Classwork Put your drills and classwork on a separate sheet of paper each day. The drills and classwork from one day will be collected each unit.

4. Cartesian Coordinate Plane ** 1.Cartesian Coordinate Plane: Composed of an x-axis (horizontal) and y-axis (vertical) which meet at the origin and divide the plane into four quadrants. 2.x – axis: The horizontal axis in the coordinate plane. 3.y – axis: The vertical axis in the coordinate plane. 4.origin: The point where the x-axis meets the y-axis corresponding the coordinate (0,0)

5. The Coordinate Plane Quadrant I ( +, + ) Quadrant II ( -, + ) Quadrant III ( -, - ) Quadrant IV ( +, - ) x y (0,0) Origin

6. Functions and Relations ** 5. relation: A set of ordered pairs. 6. domain: The set of all the x – coordinates (the 1 st numbers) of a relation. 7. range: The set of all the y – coordinates (the 2 nd numbers) of a relation. Example: Name the domain and range of the following relation: { (-1, 2), (-1, 3), (-1, 4) }

7. Mapping ** 8. mapping: Shows how each element of the domain is paired with each element of the range. Example: { (-1, 2), (-1, 3), (-1, 4) } 2 3 4 Domain Range

8. Functions ** 9.function: A special type of relation in which each element of the domain is paired with exactly one element of the range. NOTE : In a function, every x – value (input) has exactly one y – value (output). 10. discrete function: a function that consists of points that are not connected.

9. Classwork (#16)* Identify the domain and range of each mapping. State whether or not each is a function: 4.5. 2 3 DomainRange 0 1 -3 3 5 Range Domain 4

10. Vertical Line Test ** 11. Vertical Line Test: If a vertical line intersects a graph at more than one point then the relation is not a function. Pass a pencil vertically over a graph. If the pencil ever touches more than one point at a time on the graph, then the graph fails the vertical line test, and is not a function. Every x – value must have a unique y –value.

11. Continuous Functions ** 12. continuous functions: A function that can be graphed with a line or a smooth curve and has a domain with an infinite number of elements. x y (0,0) Origin 1

12. Graph each function by completing the following tables and plotting the coordinates. Then state whether each is a function. 6. y = 3x – 4 7. xy 0 1 2 xy -2 0 1 2