Function behavior of a reciprocal function?

Our teacher explained behavior function as far as increasing, decreasing, constant, and "strictly" terms for each of them. However, since the reciprocal function has a break in it, I am not sure how to define its behavior?

The function he wanted us to graph and describe the behavior of is the most basic reciprocal function, f(x)=x^(-1)

Re: Function behavior of a reciprocal function?

Hey Ascendant78.

You usually define these kinds of things as having an asymptote or being "asymptotic".

You have two kinds of asymptotes: vertical and horizontal. Vertical ones are found in the graphs like yours where you have a vertical asymptote at x = 0 for a negative one for x approaching zero from the left and a positive one for x approaching zero on the right.

The function should always be strictly decreasing everywhere but the asymptote means that it will have a break in it and this means that it will be strictly decreasing, but only with respect to the sides of where the asymptote is.

Re: Function behavior of a reciprocal function?

Great, thank you. That was something that he didn't cover in class, so good to know.