Final answer:
The parent function undefined at x = 0 is y = 1/x, which features an asymptote at this value because division by zero is undefined.
Step-by-step explanation:
The parent function that is undefined at x = 0 is the reciprocal function y = 1/x. This function is not defined at x = 0 because division by zero is undefined in mathematics. As x approaches zero, the value of y grows without bound, exhibiting a characteristic known as an asymptote. The term asymptote refers to a line that a graph approaches but never actually reaches. In the case of the reciprocal function, both the x-axis and the y-axis serve as asymptotes. Other functions may also have asymptotes or be undefined at certain points, but the reciprocal function is a classic example taught in algebra that specifically illustrates this concept at x = 0.