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Function Function Notation Function Formula y x2 y f [3( x 7)] 8 y [3x 7 ]2 8 1 2 y y 4 f [2( x 1)] y x x 1 y x y 5 f ( x) 7 y 5 x 7 y 3x y f ( 2 x) 8 y 6x 8 1.4 – Domain & Range Domain: Range: - the x-values of a relation - the y-values of a relation Determine the domain and range of the relations on the following pages. Using set notation. Two methods of expressing domain and range 1. Set Notation 2. Interval Notation What is set notation? Set Notation: A set is merely a collection of elements or members. So in math it is a collection of numbers. Set notation is like a special language that we use to express what domain and range is covered by a function. What is interval notation Interval notation is another way of defining domain and range… but it is more efficient! Open Parentheses ( ) If the value is not included or undefined. (i.e. holes, asymptotes, or a jump) Closed Parentheses [ ] If the value is part of the graph. Interval Notation Infinities or If the graph continues forever to the right or upwards, it approaches infinity. If the graph continues forever to the left or downwards, it approaches negative infinity. Union Sign If there is a break in the graph, join the interval up to and after that break with the union sign. BUT, interval notation cannot be used for discrete functions! Set Notation ‘x’ belongs to the set of real numbers Domain = {xR} Range = {yR} Interval Notation Domain : x(,) Range : y(,) Set Notation ‘y’ is less than or equal to 6 Domain = {xR} Range = {yRy6} Interval Notation Domain : [ Domain : x(,) Range : y(,6] Set Notation {(2,4), (3,5), (4,6), (5,7)} Domain = {2,3,4,5} Range = {4,5,6,7} OR OR Domain : {x I 2 x 5} Range: {y I 4 y 7} Interval Notation {(2,4), (3,5), (4,6), (5,7)} Can’t use interval notation for integers! Set Notation, because integers 3 4 -3 5 5 D: {3, 4, 5} R: {-3,5} Set Notation ‘x’ is greater than -3, but less than or equal to 5 D:{xεR | -3<x≤5} R:{yεR | y=3} Interval Notation D: R: Set Notation Domain = {xR-4x4} Range = {yR -4y4} Interval Notation Domain : x [ 4,4] Range : y [ 4,4] ‘x’ belongs to the set of integers Domain = {x-6x3} Range = {y -1y8} Set Notation Asympotote Where the graph approaches the line but never actually touches it. Interval Notation? D: R: What about equations? f ( x) 3 x 5 This is a linear function (not and not a) vertical or horizontal), so x and y can be any value. Domain = {xR} Range = {yR} b) g ( x) 2( x 1) 8 2 • This is a quadratic function. • It opens upward, thus has a min. • The min. value is -8. Domain = {xR} Range = {yRy-8} c) h( x ) x9 Are there any restrictions that must be placed on ‘x’, or will any ‘x’ value work Can’t be -’ve in this function? So, what values of ‘x’ will not make the part under the squareroot sign negative? Domain = {xRx-9} Range = {yRy0} D:X ε [-9,+∞) R: Yε [0,+∞)