Graphing Reciprocal Functions
Concept

Reciprocal Function

The reciprocal function is a function that pairs each value with its reciprocal.
Table of values of the function y=1/x
The function rule of this reciprocal function is obtained algebraically by writing the rule for the pairings shown in the table.

The graph of the function is a hyperbola, which consists of two symmetrical parts called branches. It has two asymptotes, the and axes. The domain and range are all nonzero real numbers.

Graph of y = 1/x with horizontal asymptote at y = 0 and vertical asymptote at x = 0. Points (-2, -1/2), (-1, -1), (-0.5, -2), (2, 1/2), (1, 1), and (0.5, 2) are plotted on the graph.

The graph of can be used to graph other reciprocal functions. This can be done by applying different transformations.

Name Equation Characteristics
Parent Reciprocal Function
Inverse Variation Functions
General Form of Reciprocal Functions

Extra

Reciprocal vs. Inverse of a Function

It is important not to confuse the reciprocal of a function with the inverse of a function. For numbers, refers to the reciprocal while the notation is commonly used to refer to the inverse of a function.

Function, Reciprocal, Inverse,
Exercises