Given A = {1, 2, 3, 4} B = {2, 5, 10, 17}, a E A and b E B
The mapping rule for f maps 1 to 2, 2 to 5, 3 to 10 and 4 to 17
(b) Write the mapping rule in the format of the listing method. Display the mapping using the listing format.
(c) Write the mapping rule in the format of function notation. Show the mapping using a function notation.
(d) Identify, using the most appropriate language, the type of mapping from A to B.
To answer these questions, we will go through each step one by one:
(b) Writing the mapping rule in the format of the listing method:
The mapping rule for f can be represented using the listing method as follows:
f = {(1, 2), (2, 5), (3, 10), (4, 17)}
The listing method represents the mapping by listing each element of the domain (A) with its corresponding image in the codomain (B).
(c) Writing the mapping rule in the format of function notation:
The mapping rule for f can be represented using function notation as follows:
f: A -> B, where f(1) = 2, f(2) = 5, f(3) = 10, and f(4) = 17
In function notation, we define the mapping rule using the function name (f), the domain (A) and codomain (B) separated by an arrow, and then assign the images of each element in the domain.
(d) Identifying the type of mapping from A to B:
Based on the given information, we can determine that this mapping is an example of a function. A function is a type of mapping where each element in the domain has exactly one image in the codomain. In this case, each element in set A has exactly one image in set B, making it a function.
Therefore, the type of mapping from A to B is a function.