To determine which table represents a function, we need to examine the relationship between the input ($x$) and output ($y$) values in each table. For a set of inputs and outputs to represent a function, each input should correspond to exactly one output value. In other words, no $x$ value should map to multiple $y$ values.

Let's analyze each table based on this principle:

1. Top Left Table:

   • Input ($x$): 10, 20, 30, 30, 40
   • Output ($y$): -5, -6, -7, -8, -9
   • This table has two instances of $x = 30$, which correspond to different $y$ values (-7 and -8). This violates the function rule, as one input cannot have multiple outputs. Therefore, this is not a function.

2. Top Right Table:

   • Input ($x$): -5, -5, -5, -5, -5
   • Output ($y$): 0, 5, 0, 10, 15
   • Here, the input $-5$ is repeated multiple times with different output values (0, 5, 10, 15). This also violates the function rule, so this is not a function.

3. Bottom Left Table:

   • Input ($x$): -3, -1, 0, 1, 1
   • Output ($y$): 8, 10, 12, 14, 16
   • The input $1$ is repeated with different outputs (14 and 16). This violates the function rule as well, making this not a function.

4. Bottom Right Table:

   • Input ($x$): -2, 0, 2, 4
   • Output ($y$): 6, 7, 8, 9
   • Each input has a unique output in this table. No input is repeated, and each $x$ value corresponds to exactly one $y$ value. This table does represent a function.

Conclusion

The Bottom Right Table represents a function because each input has a unique output, satisfying the definition of a function.

Would you like a further explanation of functions or have any questions?

Related Questions

1. What is the difference between a function and a relation?
2. How can we determine if a graph represents a function?
3. Why is it important for each input in a function to have a unique output?
4. Can a function have repeated output values with different inputs?
5. What are real-world examples of functions?

Tip

Remember, to verify if a table represents a function, check that each input value corresponds to only one unique output.