Which of the following equations does not represent y as a function of x in the standard (x, y) coordinate plane?

Rationale

x - y² + 2 = 0 does not represent y as a function of x in the standard (x, y) coordinate plane.

This equation explicitly relates x and y in a way that does not allow for a unique value of y for each value of x, thus failing the definition of a function.

A (y = x) YOUR ANSWER

This equation represents a linear function where for every value of x, there is a corresponding unique value of y. The relationship is direct and clearly defines y in terms of x.

B (y = x + 2) YOUR ANSWER

Similar to option A, this equation is also a linear function. It defines y as a unique value that is always 2 units greater than x, maintaining a one-to-one relationship.

C (y = x² + 2) YOUR ANSWER

This equation describes a parabola opening upwards. For each value of x, there is a unique y value, fulfilling the function criteria, as it assigns exactly one output for each input.

D (x - y + 2 = 0) YOUR ANSWER

Rearranging this equation yields y = x + 2, which is a linear function. Each x value corresponds uniquely to a y value, making it a valid representation of a function.

Conclusion

In summary, the equation x - y² + 2 = 0 does not define y as a function of x because for certain values of x, there can be multiple corresponding y values (e.g., both positive and negative square roots). In contrast, the other options (A, B, C, D) all depict valid functions where each input x leads to a unique output y, thereby satisfying the definition of a function in the coordinate plane.