chapter 8

direct variation

: mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other

joint variation

Joint variation" means "directly, but with two or more variables"

reciprocal function

a function defined on the set of nonzero reals, that sends every real number to its reciprocal

complex fraction

A complex fraction is a fraction where the numerator, denominator, or both contain a fraction. Example 1: is a complex fraction. The numerator is 3 and the denominator is 1/2. Example 2: is a complex fraction. The numerator is 3/7 and the denominator is 9.

rational expression

A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials

oblique asymptote

A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes.

rational inequality

A rational inequality is an inequality which contains a rational expression

inverse variation

An inverse variation is a situation in which one quantity increases while another quantity decreases

combined variation

Combined variation describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others (when the rest of the variables are held constant).

horizontal asymptote

The line x = a is a vertical asymptote of the function y = f(x) if y approaches ±∞ as x approaches a from the right or left. This graph has a vertical asymptote at x = 1

constant variation

The ratio between two variables in a direct variation or the product of two variables in an inverse variation. In the direct variation equations = k and y = kx , and the inverse variation equations xy = k and y = , k is the constant of variation.

vertical asymptote

Vertical asymptotes are straight lines of the equation , toward which a function f(x) approaches infinitesimally closely, but never reaches the line, as f(x) increases without bound

hyperbola

a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

weighted average

an average resulting from the multiplication of each component by a factor reflecting its importance.

rational equation

an equation in which one or more of the terms is a fractional one. When solving these rational equations

rational function

rational function is any function which can be defined by a rational fraction

point discontinuity

the graph that the function is continuous except for the tiny hole in the curve at x = 1. It is discontinuous at a single point, and this discontinuity is called a point discontinuity.