# Reciprocal Graphs

## Understanding Reciprocal Graphs

Reciprocal graphs are graphical representations of mathematical functions in the form of **y = a/x** and **y = x/b**, where **a** and **b** are real constants and **x** is a variable. These graphs are useful for visualizing relationships that exhibit inverse proportionality, meaning that as one variable increases, the other decreases.

### Asymptotes

When graphing a reciprocal function, it is essential to consider its asymptotes. Asymptotes are lines that the curve approaches but never touches. The **y = a/x** and **y = x/b** graphs have asymptotes at **x = 0** and **y = 0** respectively. A vertical asymptote represents values of **x** that cannot be divided by zero, while a horizontal asymptote represents values of **y** that cannot equal zero.

For instance, the graph of **y = a/x** is symmetric to the lines **y = x** and **y = -x**, which is crucial to consider when sketching the graph.

### Types of Reciprocal Graphs

The coordinate plane is divided into four quadrants, labeled with roman numerals (I, II, III, and IV) for visualization purposes.

**Reciprocal Functions of the Form y = a/x**

If **a** is a positive value, the graph of **y = a/x** will be drawn in quadrants I and III. For example, **y = 2/x** will have a graph like the one shown below. On the other hand, if **a** is negative, the graph will be drawn in quadrants II and IV, as shown by **y = -2/x**.

**y = 2/x**graph: <