Variation Functions 5-1/5-5

Complex fraction

A fraction that contains one or more fraction in the numerator, the denominator, or both

Discontinuous function

A function whose graph has one or more jumps, breaks, or holes

Continuous function

A function whose graph is unbroken line or curve with no gaps or breaks

Rational function

A function whose rule can be written as a rational expression

Joint Variation

A relationship among three variables that can be written in the form y=kxz, where k is a non-zero constant

Inverse variation

A relationship between two variables, x and y, that can be written in the form y=k/x, where k is a non-zero constant and x

Combined variation

A relationship containing both direct and inverse variation

Extraneous solution

A solution or a derived equation that is not a solution of the original equation

Rational expression

An algebraic expression whose numerator and denominator are polynomials and whose denominator has a degree >= 1

Rational equation

An equation that contains one or more rational expression

Rational inequality

An inequality that contains one or ore rational expressions

Hole (in a graph)

An omitted point on a graph. If a rational function has the same factor x-b in both the numerator and the denominator, and the line x+b is not a vertical asymptote, then there is a hole in the graph at the point where x=b

Direct variation

Relationship between two variable x and y that can be written in the form y=k,x, where k is a non-zero constant that behaviors like the slope. Alway grow through the origin.

Constant of Variation

The constant k in a direct variation equation