Two-dimensional graph

A two-dimensional graph is a set of points in two-dimensional space. If the points are real and if Cartesian coordinates are used, each axis depicts the potential values of a particular real variable. Often the variable on the horizontal axis is called x and the one on the vertical axis is called y, in which case the horizontal and vertical axes are sometimes called the x axis and y axis respectively. With real variables on the axes, each point in the graph depicts the values of two real variables.

Alternatively, each point in a graph may depict the value of a single complex variable. In this case, the horizontal axis is called the real axis and depicts the potential values of the real part of the complex number, while the vertical axis is called the imaginary axis and depicts the potential values of the imaginary part of the complex number.

Graph of a function

Graph of the function $f(x)={{x^{3}}-9x}\!\$

If the relation between the two real variables is of the form $y=f(x)$ where f is a function giving a single value of y associated with each admissible value of x, then the graph is called the graph of a function. The function could be a polynomial function or a transcendental function.

For example, the graph of the cubic polynomial

f(x)={{x^{3}}-9x}\!\

is

{(x, x³-9x) : x is a real number}.

If this set is plotted on a Cartesian plane, the result is a curve (see figure).

An example of a two-dimensional graph of a transcendental function is the graph of the logarithmic function at the left.

Graph of a polynomial equation in two variables

In some cases a polynomial in two variables cannot be rewritten in the form $y=f(x)$ . Nevertheless, the set of all points satisfying the equation can still be plotted as a two-dimensional graph, as in the accompanying graph of the circle <math>(x-a)^2+(y-b)^2=1.

Graph of a function

Graph of a polynomial equation in two variables

See also