Final answer:
Yes, there are planes that are not the graph of a function of x and y. These planes are vertical planes, which are parallel to the y-axis. All other planes that are not vertical are the graph of a function of x and y.
Step-by-step explanation:
Yes, there are planes that are not the graph of a function of x and y. These planes are vertical planes, which are parallel to the y-axis. In a vertical plane, every value of x corresponds to multiple values of y. This means that for a given x-value, there are multiple points on the plane with different y-values, which violates the definition of a function.
For example, the equation of a vertical plane parallel to the y-axis is x = k, where k is a constant. This equation represents a plane where every point has the same x-coordinate and different y-coordinates. Therefore, it is not the graph of a function of x and y.
On the other hand, all other planes that are not vertical are the graph of a function of x and y.