The following rational function describes concentration in blood of a certain medicine taken once depending on time, find:
A.the horizontal asymptote(s)
B.the vertical asymptote(s)
C. describe their possible meanings
Horizontal asymptote is y=-100
vertical asymptotes are x=-10, x=10
I don't understand C
It might help if you actually supplied the function.
Clearly it looks something like
-100x^2
---------------------
(x+10)(x-10)
In order to understand the possible meanings of the horizontal and vertical asymptotes, it's important to first understand what these asymptotes represent in the context of a rational function.
A rational function is a function that can be expressed as the ratio of two polynomial functions. In this case, the rational function represents the concentration in the blood of a certain medicine over time. The numerator and denominator of the rational function are not specified, but we can still analyze the asymptotes.
1. Horizontal Asymptote (y = -100):
The horizontal asymptote represents the behavior of the function as the input (time) approaches infinity or negative infinity. In this case, the specified horizontal asymptote is y = -100.
This means that as time goes on, the concentration of the medicine approaches -100 in the blood. It suggests that the medicine is gradually being flushed out of the bloodstream or becoming less effective over time. So, the possible meaning of this horizontal asymptote is that the medicine concentration tends to decrease and stabilize at a value close to -100 over an extended period.
2. Vertical Asymptotes (x = -10, x = 10):
The vertical asymptotes represent the points where the function approaches infinity or negative infinity as the input approaches these values. In this case, the vertical asymptotes are located at x = -10 and x = 10.
These vertical asymptotes imply that the medicine concentration experiences significant changes near these time points. It suggests that there might be specific intervals around -10 and 10 where the medicine concentration increases or decreases rapidly. The possible meanings could be related to the absorption or elimination of the medicine within these time intervals.
Overall, the horizontal asymptote indicates the long-term behavior of the medicine concentration in the blood, while the vertical asymptotes represent specific time points where the concentration undergoes significant changes.