Table 1
Input (x) 1 3 5 5 9
Output (y) 7 16 19 20 28
We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
From Table 1, it is clear that:
- Each input or x-value of the X set has a unique y-value or output of the Y set.
- There is no duplicated input (repeated x value).
Therefore, Table 1 represents a function.
Table 2
Input (x) 0.5 7 7 12 15
Output (y) 7 15 10 23 30
We already know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
From Table 2, it is clear that:
- There is a duplicated input (repeated x value) i.e. x = 7 appears twice. And we can not have repeated input values.
As the input x = 7 is repeated multiple times, thus, the given table 2 does not represent a function.
Therefore, Table 2 does not represent a function.