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### High School Mathematics - 24.10 Introduction to Functions

 Function Definition: A function is a relation that has exactly one "output" for every "input". Consider two sets A and B to form the Cartesian product. This Cartesian product forms the relations. Among these relations we select those relations that satisfy the condition - every element on A is related to only one element in set B. When a relation satisfies this rule we call it function. Function: Any relation on A x B in which in which every element in set A has a corresponding element on set B. It is denoted as f: A ->B or f: x -> f(x) or y = f(x) where y is a function of x. First element is also called domain, abscissa, preimage or the first component. Second element is also called range, ordinate, image or second component. A function can be represented by arrow diagram, set-builder notation, Cartesian form. Representation of a function Arrow Diagram Domain = {1,2,3,4} Range = {D,B,C,A} Set-builder Notation f = {(x,y)ly = 3x+5} Cartesian Form f = {(1,2), (2,3), (4,5)} Directions: Solve the following problems. Also write at least 5 examples of your own.
 Q 1: Which of the following relations are functions?{(1,2), (3,7), (4,-6), (8,11)}{(1,2), (1,3), (3,4), (4,5)}{(2,-3),(3,-4), (3,9), (5,8)} Q 2: Which of the following relations are functions?y > x + 5y < x+3y = 3x+2 Q 3: Let f: N -> N. If f = {(1,3), (2,5), (3,7)......}, find f(x)f(x) = 2x -1f(x) = 3x -2f(x) = 2x+1 Q 4: Write the domain of the function of F: x ->5x , X € {0,1,2}{5, 10, 15}{0, 5, 10}{0,1,2} Q 5: Let X = {1,2,3,4}. Determine whether r not each relation is a function from X to X.g = {(3,1), (4,2), (1,1)}f = {(2,3), (1,4), (2,1), (3,2), (4,4)}h = {(2,1),(4,4), (3,4)} Q 6: Write the domain of h: x-> 2/(x-7)Domain is set of all real numbersDomain is set of all natural numbersDomain is all numbers except 7 Q 7: If n(A) = p and n(B) = q, then the possible number of mappings from A to B is n?.0qp Q 8: Given that f(x) = 2x and f: N->N, find the range f .Answer: Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!