1 1 Relations and Functions Objectives Determine whether

1. 1 Relations and Functions Objectives: Determine whether a relation is a function, identify the domain and range, evaluate functions

Relation: A set of ordered pairs Domain (D): The first element in an ordered pair. (abscissa) Range (R): Ex. 1) The second element in an ordered pair. (ordinate) State the relation of the windchill data as a set of ordered pairs. State the domain and range of the relation. Windchill Factors at 20° F Wind speed (mph) Windchill temp. (° F) 5 19 10 3 15 -5 20 -10 25 -15 30 -18

Ex. 2) The domain of a relation is all consecutive integers between -2 and 2. The range y of the relation is 2 less than twice x, where x is a member of the domain. Write the relation as a table of values and as an equation. Then graph the relation. X -1 0 1 Y y = 2 x - 2

Ex. 3) State the domain and range of each relation. a. ) b. ) Function: A relation in which each element of the domain is paired with exactly one element of the range. (A set of ordered pairs in which no two pairs have the same first element. )

Ex. 4) Vertical Line Test: State the domain and range of each relation and if it is a function. a. ) {(-2, 0), (3, 2), (4, 5)} b. ) {(-3, -2), (-2, -2), (-1, -2), (0, -2)} A test to see if a relation is a function. If a vertical line touches a graph more than once it is not a function. Ex. 5) Determine if the graph is a function. a. ) b. )

Function Notation: An equation of y in terms of x can be rewritten so that y =f(x). “f of x” Ex. 6) Ex. 7) State the domain of each function a. ) f(x) = x² + 2 x b. ) g(x) = √(x + 4) x+1 x² - 4