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### High School Mathematics - 24.9 Functions

 A function is a relation (usually an equation) in which no two ordered pairs have the same x-coordinate when graphed. One way to tell if a graph is a function is the vertical line test, which says if it is possible for a vertical line to meet a graph more than once, the graph is not a function. Functions are usually denoted by letters such as f or g. If the first coordinate of an ordered pair is represented by x, the second coordinate (the y coordinate) can be represented by f(x). When a function is an equation, the domain is the set of numbers that are replacements for x that give a value for f(x) that is on the graph. Example 1: For f(x) = 2x+6, find f(5) f(x) = 2x+6 = 2x5+6 = 10 + 6 = 16 Example 2: Find the domain of the function f(x) = 4/x x can take any value except zero. Since division by 0 is not defined. Therefore, the domain is said to be x > 0 and x < 0. Directions: Answer the following questions. Also write at least 10 examples of your own.
 Q 1: Given that f(x) = 2x and f: N->N, Check if f(2) + f(3) = f(2+3)yesno Q 2: For f(x) = 2x, find f(5x)10x5x8x Q 3: If f = {(1,2), (2,-3), (3,1)} is a function, find 2+f{(3,2),(4,-3), (5,1)}{1,4), (2,-1), (3,1)}{(2,4), (3,4), (3,5)} Q 4: If f is a real; function, find the domain of f(x) = 10-x01R Q 5: For x>3, if f(x) = 3x -2 , g(x) = x2-2, find f3(3x-2)(2x-1)3(2x-1) Q 6: Let x = {2,3}, Y = {1,3,5}, ow many different functions are there from X into Y.975 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!