Which of the following tables represents a relation that is a function?

Question

x y
−5 −3
−2 3
−1 1
3 4
3 −1
x y
−5 4
−2 4
0 −4
0 4
3 4
x y
−4 0
−2 2
0 3
2 0
3 4
x y
1 −4
1 −2
1 0
1 2
1 4

Answer 1

A relation is considered a function if each input (x-value) corresponds to exactly one output (y-value). Let's analyze each of the provided tables to determine which one represents a function:

1. Table 1:

   x     y
   −5   −3
   −2    3
   −1    1
    3    4
    3   −1
   

   • The x-value 3 appears twice (with y-values 4 and -1). This means that a single x-value corresponds to two different y-values. Therefore, this table does not represent a function.

2. Table 2:

   x     y
   −5    4
   −2    4
   0    −4
   0    4
   3    4
   

   • The x-value 0 appears twice (with y-values -4 and 4). This means that a single x-value corresponds to two different y-values. Therefore, this table does not represent a function.

3. Table 3:

   x     y
   −4    0
   −2    2
   0     3
   2     0
   3     4
   

   • All x-values are unique, and each x-value corresponds to exactly one y-value. Therefore, this table represents a function.

4. Table 4:

   x     y
   1    −4
   1    −2
   1     0
   1     2
   1     4
   

   • The x-value 1 appears multiple times (with different y-values -4, -2, 0, 2, and 4). This means that a single x-value corresponds to multiple different y-values. Therefore, this table does not represent a function.

In conclusion, only Table 3 represents a relation that is a function.