Given the function f = {(1, 2), (2, 3), (3, 4)} write the set of ordered pairs representing f".

Given that A = {1, 2, 3, 4, 5} and B = {x, y, z}, determine which of the sets of ordered pairs represents a function from A to B. Explain the reason(s) why or why not for each i)  {(1, z), (2, x), (3, y), (2, x)} ii)  {(1, z), (3, y), (2, x), (4, x), (5, 5)} iii)  {(1, y), (2, y), (5, x), (3, y), (4, y)} Which of the following graphs represent y as a functionof x? Explain the reason(s) why or why not for each ii)

(1a) Let A = {1, 6, 12}, B = {0, 2, 12}. The following are all relations from A to B, but which are functions? Explain why or why not? f1 = {(1, 2),(6, 0),(12, 12)} f2 = {(1, 0),(1, 2),(6, 12),(12, 0)} f3 = {(1, 12),(6, 0)} f4 = {(1, 0),(6, 0),(12, 2)}   (1b) Let X = {a, b, c, x, y, z} and Y = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Define a function f : X → Y to be: f = {(a, 2),(b, 3),(c, 7),(x, 9),(y, 4),(z, 8)}. Define a function g : Y → X to be: g = {(1, b),(2, c),(3, b),(4, a),(5, z),(6, z),(7, b),(8, x),(9, y)}. Determine the following: 1. The range of f. 2. The range of g. Do we have Rng(f) a proper subset of Codom(f)? What about for g?

Which of the following set is not a function? a. D = {(8,2), (-1,5), (-5,2), (5,0)} b. B = {(3,2), (1,5), (-4,2), (5,0)} C. Z = {(-3,2), (1,5), (-3,2), (1,0)} d. A = {(3,2), (7,4), (-7,2), (5,0)}