Final answer:
A vertical asymptote is a line a function approaches but never intersects as the x-value nears a certain point, typically where the function is undefined. For y = 1/x, this occurs at x=0, where y tends toward infinity.
Step-by-step explanation:
A vertical asymptote is a line that a function approaches but never touches as the independent variable (usually x) approaches a certain value. For the function y = 1/x, a vertical asymptote occurs at x=0 because as x approaches zero, the y-value increases or decreases without bound, approaching infinity. Most often, vertical asymptotes occur at points where the denominator of a rational function is zero, leading to an undefined value for the function at that x-value.
In graphical terms, the curve of the function becomes closer and closer to the vertical line of the asymptote as it moves along the x-axis, but it never actually intersects with the asymptote line, no matter how far the curve is followed. It's important to note that for a vertical asymptote x-value, the function itself does not have a y-value; it is merely an indication of a boundary the function will infinitely approach as x moves closer to that value.