Find four relations from {a, b} to {x, y} that are not functions from {a, b} to {x, y}.

(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?

a. Find all functions from {0, 1} to {1}.b. Find two relations from {0, 1} to {1} that are not functions.

Is the relation shown in the table below a function? (type in yes or no) \table[[x,y],[-2,4],[-1,7],[0,10],[1,7]]

Which of these pairs of the form (x, y) could not lie on the graph of a function of x? O (2, 1) and (2, 2) O (2, 1) and (3, 1) O (2, 2) and (3, 2) O (1, 1) and (2, 2)

Let f {(0,-3),(9,4),(-6,9)} and h = {(-6,4), (-3,9)}. Find fo h. foh= (Use a comma to separate ordered pairs as needed.)

State why the function 2z2 - 3z + e-z is analytic everywhere.

Determine if each of the following relations is a functions with domain A= {1,2,3,4} and codomain B={a,b,c,d}. Give a brief reason. (1) f = {(1,d),(2,d),(3,b)} . (2) g = {(1,d),(2,c), (3,c), (3,a),(4, d)}.