Lesson 1: Inverse Variation and the Reciprocal Function

Property

$y$ varies inversely with $x$ if

where $k$ is a positive constant. This relationship implies that the product of the variables is constant: $xy = k$.

Property

The reciprocal function is $f(x) = \frac{1}{x}$. An asymptote is a line that the graph of a function approaches but never touches. For the reciprocal function, the y-axis ($x=0$) is a vertical asymptote, and the x-axis ($y=0$) is a horizontal asymptote.

Examples

Property

To graph reciprocal functions of the form $y = \frac{k}{x}$, create a table of values avoiding $x = 0$, plot the points, and connect them with smooth curves that approach but never touch the asymptotes at $x = 0$ and $y = 0$.

Examples