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Relations and Functions 9.2 Relations 9.5 Functions

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F E LineSlopeY-interceptSI Y=mx+b SF Ax + By=C E F You may count the slope or Pick two points and use calculator

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Ex 1 Find the distance between the points P(2, 2) and Q (4, -6). Work inside parentheses Do powers before doing the addition!!!!!! Be careful Of Signs!!! (neg) 2 = POS.

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Ex 5 Find the midpoint whose endpoints are (1, -2) and (-17, 16)

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Ex 8 M(-8, 7) is the midpoint of RS. If S has a coordinates (-6, 8), find the coordinates of R. R (x 1, y 1 ) S (-6, 8) M(-8, 7)

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Topics Domain Range Mapping Inverse of a Relation Functions (relation/graphs) Function Notation Evaluate Function

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Relations (sets of ordered pairs) Ways to display a relation List the set of ordered pairs Graphing Table Mapping

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XY 22 57 4 96 Table Mapping 2 5 7 -1 4 9 6 Graphing 2 5 7 -1 4 9 6 2 5 7 -1 4 9 6 2 5 7 -1 4 9 6 2 5 7 -1 4 9 6

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Domain Range The domain of a relation is the set of all the first coordinates from the ordered pairs. The x values The Range is the set of all the second coordinates from the ordered pairs. The y values A set of ordered pairs {(2,-2), (-2,3), (5,7), (4,8)} Domain { 2, -2, 5, 4} Range {-2, 3, 7, 8} Ordered pairs in parentheses Sets denoted by brackets

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Ex 1 List the ordered pairs, domain, range, and inverse XY 02 16 -5-2 123 A set of ordered pairs {(0,2), (1,6), (-5,-2), (12,3)} Domain { 0, 1, -5, 12} Range {2, 6, -2, 3} Inverse {(2,0), (6,1), (-2, -5), (3, 12)} What is domain? X-values What is Range? y-values Inverse---switch x and y

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Ex 2 List the ordered pairs, domain, range, and inverse XY 8-3 49 11 -137 A set of ordered pairs {(8,-3), (4,9), (1,1), (-13,7)} Domain { 8, 4, 1, -13} Range {-3, 9, 1, 7} Inverse {(-3,8), (9,4), (1,1), (7,-13)} What is domain? X-values What is Range? y-values Inverse---switch x and y

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Definition of a function Function is a special relation where each “x” is paired with exactly one “y” {(2,3) (4,5) (2,8)} {(5,8), (2, 9), (3,9)} Another way to say it X’s are girls y’s are boys Girls can’t cheat on a boy but a boy can cheat on a girl Not a function Yes, a function Boys can cheat

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Examples 3-6 Which are functions? #3 {(-9,4) (2,6) (3,8), (3,9)} #4 {(4,6), (12, 9), (2,3), (4,6)} #5 {(1,3) (14,15) (12,8), (14,5)} #6 {(-5,8), (7, 8), (3,9)} NO YES NO YES

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Vertical Line Test-- Can’t touch line more than once or not a function Not a function Yes! It’s a function Not a function

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Examples 7-10 YES NO YES # 9

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Function Notation y=2x + 6 F(x) =2x + 6 Read “f of x” Represents the value in the range for that particular value of x F(3) is the function value for f for x=3. Plug the 3 in for x F(3) = 2(3) + 6 F(3)= 6 + 6 = 12 Can write it as (3,12)

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Ex 10-12

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