Which relation(s) best shows `y` as a function of `x`? (Select all that apply.)

To determine which relations show y as a function of x, we must check if each x value corresponds to exactly one y value (i.e., there are no repeated x values with different y values).

Let's evaluate each option:

A. (-1,2), (3, -4), (-1,7), (0,9)

• The x value -1 appears twice with different y values (2 and 7). Therefore, A is not a function.

B. (1,6), (3,4), (-1,3), (0,-5)

• All x values (1, 3, -1, 0) are unique. Therefore, B is a function.

C. (1,2), (3,2), (-1,2), (0,2)

• All x values (1, 3, -1, 0) are unique. Therefore, C is a function.

D. (-5,8), (8,4), (-2,5), (0,-4)

• All x values (-5, 8, -2, 0) are unique. Therefore, D is a function.

E. (1,7), (3,4), (1,-3), (2,-6)

• The x value 1 appears twice with different y values (7 and -3). Therefore, E is not a function.

F. (9,2), (0, -4), (-1,6), (9,-8)

• The x value 9 appears twice with different y values (2 and -8). Therefore, F is not a function.

In summary, the relations that show y as a function of x are:

• B
• C
• D