# Graphs of important non-linear functions

**Quadratic functions**

A quadratic function always contains the *x*² term and a *x* and the shape of the graph is called a parabola. For example:

**Cubic functions**

A cubic function always contains the *x*³ term and can also have an *x*² or *x* or a constant. The shapes of cubic graphs are as follows:

**Reciprocal functions**

A reciprocal function always contains a fraction with a term in *x* in the denominator. In the example below, the axes form asymptotes as the curve never crosses or touches the *x* or *y* axis. For example:

**Exponential functions**

An exponential function is a function in the form of *y* = *a*ª, where a is a positive constant. This function produces an asymptote graph as shown below:

**The equation of a circle**

The equation of a circle is *x²* + *y²* = *r² *and is represented as follows:

Point to note: The equation of a circle is not called an equation but a locus.