Precalc0101to0102-page4

Precalc0101to0102-page4 - cannot allow one input to yield...

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(Section 1.1: Functions) 1.1.3 Example 2 (A Relation that is a Function; Revisiting Example 1) Again, let the relation R = 1, 5 () , ± ,5 () ,5 ,7 () {} . Determine whether or not the relation is also a function . If it is a function, find its domain and its range . § Solution Refer to the arrow diagram in Example 1. Each input is related to (“yields”) exactly one output. Therefore, this relation is a function . • Its domain is the set of all inputs : ± ,5 {} . • Its range is the set of all outputs : 5, 7 {} . •• Do not write 5, 5, 7 {} . § WARNING 3 :
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Unformatted text preview: cannot allow one input to yield multiple outputs, a function can allow multiple inputs (such as 1 and in Example 2) to yield the same output (5). However, such a function would not be one-to-one (see Section 1.9). Example 3 (A Relation that is Not a Function) Repeat Example 2 for the relation S , where S = 5,1 ( ) , 5, ( ) , 7, 5 ( ) { } . Solution S can be represented by the arrow diagram below. An input (5) is related to (yields) two different outputs (1 and ). Therefore, this relation is not a function....
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