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Chapter 8: Problem 50

Give an example of a relation with the following characteristics: The relation is a function containing two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function.

Short Answer

Expert verified
A good example could be the pairs (1,2) and (3,2).

Step by step solution

01

- Understanding the criteria

The first important fact to acknowledge is that a function, by definition, only has one unique output for each input. Therefore, we have to pick two pairs (a,b) and (c,d) which fulfill this criterion. This means a cannot be equal to c, because otherwise there would be two outputs for one input in the function, which isn't allowed.
02

- Ensuring reverse isn't a function

Next, note that when we reverse these ordered pairs, they should result in a relation that isn't a function. If the reverse isn't to be a function then we are looking for a case where there could be multiple outputs for the same input, which is the definition of relations that are not functions. So the condition here would be b = d.
03

- Choosing the right ordered pairs

With these conditions in mind, we can choose any ordered pairs that satisfy both these conditions. For instance, the pairs (1,2) and (3,2) would serve as a valid example. They form a function because the first components are different. When reversed to (2,1) and (2,3), however, they do not form a function because the input 2 now has two different outputs - 1 and 3.

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Most popular questions from this chapter

Graph each of the three functions in the same \([-10,10,1]\) by \([-10,10,1]\) viewing rectangle. \(y_{1}=x\) \(y_{2}=x-4\) \(y_{3}=y_{1} \cdot y_{2}\)

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