Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
Yes, it is a function. Since every element in the domain has one and only one image, this relation satisfies the definition of a function. Domain = {2, 5, 8, 11, 14, 17}. Range = {1}.
Yes, it is a function. Since every element in the domain has one and only one image, this relation satisfies the definition of a function. Domain = {2, 4, 6, 8, 10, 12, 14}. Range = {1, 2, 3, 4, 5, 6, 7}.
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No, it is not a function. The element 1 in the domain corresponds to two different images (3 and 5). According to the definition, a relation is a function only if every element has one and only one image.
Explanation
The textbook defines a function as 'a relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B.' In Example 11, similar reasoning is applied: (i) is a function because elements have unique images, (ii) is not a function because 'the same first element 2 corresponds to two different images 2 and 4.' This pattern directly applies to the three parts of this question.