Final answer:
The reciprocal function y = 1/x has end behavior limits, where y approaches infinity as x approaches zero, and y approaches zero as x approaches infinity, demonstrating the function's vertical and horizontal asymptotes.
Step-by-step explanation:
The reciprocal function, represented as y = 1/x, is a function with interesting end behavior. As we explore this function, it's crucial to consider its behavior as the variable x approaches both infinity and zero to understand its asymptotes. As x approaches zero, the function value of y grows without bound, heading towards positive or negative infinity depending on the direction from which x is approaching zero. Conversely, as x approaches infinity, the value of y approaches zero, indicating that the x-axis is a horizontal asymptote.
When expressing answers in mathematics, such as limits and asymptotic behavior, it is important to use the correct number of significant figures and proper units; however, for reciprocal functions, these concerns are less about numerical precision and more about the concept of limits. In the case of a reciprocal function, we do not have a unit per se, because we are discussing behavior in terms of 'approaching' rather than specific values.
Now, if we think about increasing the number of values generated to 500 instead of 50 as suggested by the student's question, this increment would result in a more detailed graph. Such a graph would more closely resemble the smooth curve that depicts the theoretical behavior of y = 1/x, highlighting the asymptotic nature even more clearly due to the increase in data points depicting the function's behavior.