Function as Mapping Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Which of the following sets of ordered pairs defines a function from {1,2,3}\{1,2,3\} to R\mathbb{R}? (A) {(1,5),(2,5),(3,5)}\{(1,5),(2,5),(3,5)\} (B) {(1,2),(2,3)}\{(1,2),(2,3)\} (C) {(1,0),(2,1),(3,2),(1,4)}\{(1,0),(2,1),(3,2),(1,4)\}

Solution

  1. 1
    (A): Each of 1,2,31,2,3 appears exactly once as a first element. Valid function (constant function).
  2. 2
    (B): Element 33 from the domain has no image. Not a function (undefined for x=3x=3). (C): 11 appears twice with different outputs (0(0 and 4)4). Not a function.

Answer

Only (A) is a function
A valid function must assign exactly one output to every element of the domain. (B) fails because 33 has no image; (C) fails because 11 has two images. Only (A) satisfies both conditions.

About Function as Mapping

Viewing a function as a mapping means thinking of it as an explicit association from each element of the domain to exactly one element of the codomain.

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More Function as Mapping Examples

Example 1 easy

Let [formula] be defined by [formula], [formula], [formula]. Determine whether [formula] is a valid

Example 2 medium

Explain why the relation [formula] is NOT a function from [formula] to [formula].

Example 4 medium

Let [formula], [formula]. Find [formula] (the pre-image of [formula]) and explain why [formula] does

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