Final answer:
The function y = 1/x has a horizontal asymptote at y=0 and a vertical asymptote at x=0, so the correct answer is C.
Step-by-step explanation:
The question involves finding the horizontal and vertical asymptotes of the function y = 1/x. Asymptotes are lines that the graph of a function approaches but never touches. Horizontal asymptotes indicate the value that y approaches as x goes to infinity, while vertical asymptotes indicate the value that x approaches that forces y to become unbounded. For the function y = 1/x, as x approaches zero from either direction, the value of y becomes unboundedly large or small (it goes to infinity or negative infinity), indicating a vertical asymptote at x=0. Conversely, as x increases or decreases without bound, the value of y approaches zero, which suggests a horizontal asymptote at y=0.
To find the horizontal and vertical asymptotes for a function, we need to analyze the behavior of the function as x approaches infinity and as x approaches negative infinity.
For the given options, the correct answer is D) Horizontal: None; Vertical: y=0.
Since the function given does not have any term with x in the denominator, it doesn't have a horizontal asymptote. As x approaches infinity or negative infinity, the function approaches y = 0, which indicates a vertical asymptote.
Therefore, the correct answer is C: Horizontal: y=0; Vertical: x=0.