chapter 8.

complex fraction

a fraction where the numerator, denominator, or both contain a fraction

reciprocal function

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

point discontinuity

A function is said to have a point of discontinuity at x = a or the graph of the function has a hole at x = a, if the original function is undefined for x = a, whereas the related rational expression of the function in simplest form is defined for x = a.

oblique asymptote

The degree of the numerator and degree of the denominator determine whether or not there are any horizontal or oblique asymptotes.

constant of 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.

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, we utilize one of two methods that will eliminate the denominator of each of the terms.

rational function

any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers, they may be taken in any field K.

vertical asymptote

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. For these values of x, the function is either unbounded or is undefined.

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).

joint variation

directly, but with two or more variables". An example would be the formula for the area of a triangle with base "b" and height "h": . In words, "the area A varies jointly with b and h"; the constant of variation is k = 1/2.

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.

horizontal aysmptote

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

inverse variation

mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.

rational expression

nothing more than a fraction in which the numerator and/or the denominator are polynomials.

hyperbola

the pair of hyperbolas formed by the intersection of a plane with two equal cones on opposites of the same vertex.

rational inequality

you first find the zeroes (from the numerator) and the undefined points (from the denominator). You use these zeroes and undefined points to divide the number line into intervals. Then you find the sign of the rational on each interval.