Drill 10 List the relation set of ordered

Drill #10 List the relation (set of ordered pairs) and the domain and range of the following mapping: 1. y x 0 -1 2 3 4 Find the value of the following if f(x) = 2. f( 2 ) 4. f(-1) 3. f( ½ ) 5. f (-¾ )

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. Homework: 2 -1 Skills Practice, #1 -14

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

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

Relation, Domain, and Range relation: A set of ordered pairs. domain: The set of all the x – coordinates (the 1 st numbers) of a relation. For a function, it’s the set of all possible values of x. range: The set of all the y – coordinates (the 2 nd numbers) of a relation. For a function, it’s the set of all possible values of y. Example: Name the domain and range of the following relation: { (-1, 2), (-1, 3), (-1, 4) }

Mapping mapping: Shows how each element of the domain is paired with each element of the range. Example: { (-1, 2), (-1, 3), (-1, 4) } D -1 2 3 4 R

Functions function: A special type of relation in which each element of the domain is paired with exactly one element of the range. (no x- values are repeated) NOTE : In a function, every x – value (input) has exactly one y – value (output). discrete function: a function that consists of points that are not connected.

Continuous Functions 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. 1 x -1 (0, 0) Origin y

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.

Mapping: Classwork Identify the domain and range of each mapping. State whether or not each is a function: A. B. -1 0 1 D 2 3 R D -3 -1 5 3 4 R

Classwork Draw a mapping of the following relations. State the a) Domain, b) Range of each set. A) {(1, 2), (1, 3), (1, 4)} B) {(2, 3), (-1, 3), (1, -3)}

One to One* One to One Functions: A function such that each element of the domain is paired with exactly one unique element in the range. One to one -1 0 1 D 2 One to one -3 3 4 R 5 D Not one to one -1 2 -1 3 3 3 4 4 R D R

Onto* Onto Functions: A function such that each element of the range is paired with exactly one unique element in the domain. Onto -1 0 1 D Onto (not a function) 2 -3 3 4 R 5 D Not onto -1 2 -1 3 4 3 D 5 R 4 R

One to One and Onto* One to one and onto: Each element of the domain is paired with a unique range value, and all range values are paired with a domain value. One to one and onto 2 -1 0 1 D 3 One to one not onto -3 -1 2 -1 4 3 4 6 D 4 R Not one to one Onto D R R

Horizontal Line Test: If a horizontal line intersects a graph at more than one point then the relation is not one to one. 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 y – value must have a unique x –value.

Evaluating functions 2 -1 Study Guide. Read 2 -1 Study Guide. Make an x-y chart for #1 – 3. Graph each point. x -3 -2 -1 0 1 2 3 f(x)