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

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 x- axis (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 y- axis corresponding the coordinate (0,0)

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

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 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. x y (0,0) Origin 1

Vertical Line Test 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. 2 3 DR R D 4

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 One to oneNot one to one D R DR DR

Onto* Onto Functions: A function such that each element of the range is paired with exactly one unique element in the domain. Onto Onto Not onto (not a function) D R DR DR

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 One to one Not one to one and ontonot onto Onto D R DR DR

Horizontal Line Test 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. xf(x)