Question 41

x - y^2 + 2 = 0 does not represent y as a function of x.

This equation involves y squared, which means for certain values of x, there can be two corresponding values of y, violating the definition of a function.

A) y = x

This equation clearly represents y as a function of x, as each value of x corresponds to exactly one value of y. Specifically, for any given x, y is simply equal to that x.

B) y = x + 2

Similar to option A, this equation defines y in terms of x, where each x value has a unique y value. Therefore, y is a function of x in this case.

C) y = x² + 2

This equation also represents y as a function of x. For every value of x, there is a single corresponding value of y, which confirms that y is a function of x.

D) x - y + 2 = 0

This equation can be rearranged to y = x + 2, which clearly shows that y is expressed uniquely as a function of x. Thus, it meets the criteria for being a function.

E) x - y² + 2 = 0

This equation can be rearranged to y² = x + 2, which indicates that for certain values of x, there are two possible values for y (positive and negative roots). This means it does not represent y as a function of x.

Conclusion

The equation x - y² + 2 = 0 fails to meet the criteria of a function since it allows for multiple y values for a single x value. In contrast, all other options clearly define y as a unique output for each input x, adhering to the definition of a function.