Family of curves

A family of curves, also function band, function band or parametric function is a lot of different curves, the mapping rules are different in at least one parameter. Special case is the tuft, a one-parameter family, and the bundle, a flock with a common point to all functions.

Definition

The crowd is a lot of points on a curve, curves on a surface or surfaces in space, each described by an equation or a system of equations with variable parameters.

According to another definition results in a set of curves from the graph of a function in which a free parameter of the function in question is varied in parameter representation.

To illustrate multitudes of function is particularly dynamic geometry systems are suitable.

• Is it for all graphs of the family of functions are straight, then one speaks of a family of straight lines. Thereby run the individual lines also parallel, so they are called parallel class.
• If all lines intersect at one point involved, there is a line bundle.
• If all lines intersect at one point involved both as also lie in a plane, there is a pencil of lines.

• If it is at all curves of the family to parabolas, one speaks of a family of parabolas.

Examples

• All the curves corresponding to the function curves are parallel to the axis ( straight line ). The curves of this parameter.
• All the curves belonging to the family of functions are parabolas through the origin ( see figure). The parameter is.
• All the curves corresponding to the relation crowd are concentric circles. The parameter is here.

• Analysis