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The cartesian products is written as A x B Exercises A1 The cartesian products is written as A x B 1. A = {3,4 ,5} and B = { x , y } 1.A x B = { (3 ,x),(3,y),(4,x),(4,y),(5,x),(5,y)} A = {6,8} and B {1,4,7} 2.A x B = { (6 ,1),(6,4),(6,7),(8,1),(8,4),(8,7)} 3. A = {1,5,7,9} and B = { 2 , 5 } 3.A x B = { (1 ,2),(1,5),(5,2),(5,5),(7,2),(7,5) ,(9,2),(9,5)} 4. A = {m,n} and B {2,4,8} 4.A x B = { (m ,2),(m,4),(m,8),(n,2),(n,4),(n,8)} 5. A = {3,6,9} and B = { 1 , 2 , 5 } 5.A x B = { (3 ,1),(3,2),(3,5),(6,1),(6,2),(6,5),(9,1) ,(9,2),(9,5)}

Relations & Functions Relation: a set of ordered pairs Domain: the set of x-coordinates Range: the set of y-coordinates When writing the domain and range, do not repeat values.

Relations and Functions Given the relation: {(1, 2), (2, 3), (2, 4), (3,4), (1, 3), (3, 1)} State the domain: D: {1, 2, 3} State the range: R: {1,2, 3, 4}

Relations and Functions Given the relation: {(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)} State the domain: D: {0,1, 2, 3} State the range: R: {-6, 0, 4}

Do the ordered pairs represent a function? Example 1 Do the ordered pairs represent a function? writing the domain and range, do not repeat values. r = {(-2, 5), (5,7), (0,1), (4, -2)} Solution -2 5 4 5 7 1 -2 Yes, no x-coordinate is repeated.

Do the ordered pairs represent a function? Example 2 Do the ordered pairs represent a function? writing the domain and range, do not repeat values. r = {(-5, 3), (0,3), (6, 3)} -5 6 Solution 3 Yes, no x-coordinate is repeated.

Do the ordered pairs represent a function? Example 3 Do the ordered pairs represent a function? writing the domain and range, do not repeat values. r = {(0, 1), (0,2), (1, 3), (2,4)} Solution 1 2 3 4 1 2 No, 0 is repeated in the domain.

Do the ordered pairs represent a function? Example 4 Do the ordered pairs represent a function? writing the domain and range, do not repeat values. Mathematics English Thai Science Edwin Richard john No, Edwin is repeated in the domain.

Mapping {(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} 2 1 3 -6 4

Functions A function is a relation in which the members of the domain (x-values) DO NOT repeat. So, for every x-value there is only one y-value that corresponds to it. y-values can be repeated.

Functions Discrete functions consist of points that are not connected. Continuous functions can be graphed with a line or smooth curve and contain an infinite number of points.

Do the ordered pairs represent a function? {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} No, 3 is repeated in the domain. {(4, 1), (5, 2), (8, 2), (9, 8)} Yes, no x-coordinate is repeated.

Exercises 4.1 Page 124 3.We find that the following diagram Homework Page 124 3.We find that the following diagram Relationship is a function ? 1 2 a b c 1 2 3 a b c 1 2 3

Exercises 4.1 Page 124 3.We find that the following diagram Relationship is a function ? 3 a b C d 1 2 3 4 4 a b C d 1 2 3 4

a b d c 1 2 4 3 a b c d e 1 2 4 3 A B A B Exercises 4.1 Page 125 4.Relationship given in tabular form. Relationship is a function ? 2 A B a b d c 1 2 4 3 1 A B a b c d e 1 2 4 3

a d c 1 2 3 a b c d e 1 3 2 4 5 A B A B Exercises 4.1 Page 125 4.Relationship given in tabular form. Relationship is a function ? 4 A B a d c 1 2 3 3 A B a b c d e 1 3 2 4 5

5.Do the ordered pairs represent a function? Exercises 4.1 Page 125 5.Do the ordered pairs represent a function? writing the domain and range, do not repeat values. 1. {(2,10), (3,15), (4, 20)} 2. {(-7,3), (-2,1), (-2, 4), (0,7)} 3. {(-2,1), (2,1), (4, 1), (-3,1)} 4. {(5,0), (3,-1), (0, 0), (5,-1), (3, -2)}

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