Question

The table shows a relation. Which statement about the relationship is correct? Input Output -1 2 3 -1 1 2 a. The relation is a function because each input has exactly one output. b. The relation is a function because each output has exactly one input. c. The relation is not a function because one input has more than one output. d. The relation is not a function because one output has more than one input.

Answer 1

The relation is not a function because one input has more than one output (Option c).

Step-by-step explanation:

A function is a special type of relation where each input value is associated with only one output value. In this case, looking at the given table, we observe that the input value of 3 is associated with two different output values, -1 and 2. This violates the definition of a function, as one input having more than one output means that the relation is not a function (Option c).

To elaborate further, for a relation to be a function, it must pass the vertical line test. The vertical line test states that no vertical line should intersect the graph of the relation more than once. In the context of a table, it means that each input should have only one corresponding output. In this scenario, since the input value of 3 has two different output values, the relation fails the vertical line test, indicating that it is not a function.

In conclusion, the correct statement is that the relation is not a function because one input (3) has more than one output. This identifies a fundamental characteristic of functions, and the violation of this criterion renders the given relation not a function.