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5.2 Relations & Functions

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5.2 – Relations & Functions Evaluating functions Remember, the DOMAIN is the set of INPUT values and the RANGE is the set of OUTPUT values. y = 3x + 4 inputoutput

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Another way to remember them is… The domain is the set of 1st coordinates of the ordered pairs. The range is the set of 2nd coordinates of the ordered pairs. A relation is a set of ordered pairs.

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Given the relation {(3,2), (1,6), (-2,0)}, find the domain and range. Domain = {3, 1, -2} Range = {2, 6, 0}

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The relation {(2,1), (-1,3), (0,4)} can be shown by either…… 1) a table. 2) a mapping. 3) a graph. xy 2 0 134134 2 0 134134

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Given the following table, show the relation, domain, range, and mapping. x-1047 y36-13 Relation = {(-1,3), (0,6), (4,-1), (7,3)} Domain = {-1, 0, 4, 7} Range = {3, 6, -1, 3}

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Mapping x-1047 y36-13 You do not need to write 3 twice in the range! 0 4 7 3 6

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What is the domain of the relation {(2,1), (4,2), (3,3), (4,1)} 1. {2, 3, 4, 4} 2. {1, 2, 3, 1} 3. {2, 3, 4} 4. {1, 2, 3} 5. {1, 2, 3, 4} Answer Now

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What is the range of the relation {(2,1), (4,2), (3,3), (4,1)} 1. {2, 3, 4, 4} 2. {1, 2, 3, 1} 3. {2, 3, 4} 4. {1, 2, 3} 5. {1, 2, 3, 4} Answer Now

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Inverse of a Relation: For every ordered pair (x,y) there must be a (y,x). Write the relation and the inverse. Relation = {(-1,-6), (3,-4), (3,2), (4,2)} Inverse = {(-6,-1), (-4,3), (2,3), (2,4)} 3 4 -6 -4 2

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Write the inverse of the mapping. -3 4 3 2 1. {(4,-3),(2,-3),(3,-3),(-1,-3)} 2. {(-3,4),(-3,3),(-3,-1),(-3,2)} 3. {-3} 4. {-1, 2, 3, 4} Answer Now

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Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x). f(x)f(x) x y

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Function Notation Output Input Name of Function

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Determine whether each relation is a function. 1.{(2, 3), (3, 0), (5, 2), (4, 3)} YES, every domain is different! f(x)f(x) 23 f(x)f(x) 30 f(x)f(x) 52 f(x)f(x) 43

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Determine whether the relation is a function. 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)} f(x)f(x) 41 f(x)f(x) 52 f(x)f(x) 53 f(x)f(x) 66 f(x)f(x) 19 NO, 5 is paired with 2 numbers!

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Is this relation a function? {(1,3), (2,3), (3,3)} 1. Yes 2. No Answer Now

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Vertical Line Test (pencil test) If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions? FUNCTION! NOPE!

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Vertical Line Test NO WAY! FUNCTION! NO!

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Is this a graph of a function? 1. Yes 2. No Answer Now

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Given f(x) = 3x - 2, find: 1) f(3) 2) f(-2) 3(3)-2 3 7 3(-2)-2 -2-8 = 7 = -8

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Given h(z) = z 2 - 4z + 9, find h(-3) (-3) 2 -4(-3)+9 -330 9 + 12 + 9 h(-3) = 30

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Given g(x) = x 2 – 2, find g(4) Answer Now 1. 2 2. 6 3. 14 4. 18

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Given f(x) = 2x + 1, find -4[f(3) – f(1)] Answer Now 1. -40 2. -16 3. -8 4. 4

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5.2 – Relations & Functions Example: Evaluate the function rule f(a) = -3a + 5 to find the range of the function for the domain {-3, 1, 4}.

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5.2 – Relations & Functions To solve this, all you have to do is plug ALL of the numbers in for a and solve. f(a) = -3a + 5 f(-3) = -3(-3) + 5 f(-3) = 9 + 5 f(-3) = 14

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5.2 – Relations & Functions Once you have done this for ALL of the numbers, you would write your answer from smallest to largest like the following: {-7, 2, 14}

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5.2 – Relations & Functions Make a table for f(n) = -2n + 7. Use 1, 2, 3, and 4 as domain values. 2 nf(n) 1 2 3 4

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