Unit 8 Vocabulary

Complex Fraction

A complex fraction is a fraction where the numerator, denominator, or both contain a fraction.

Joint Variation

Joint variation is a variable which is proportional to the product of two or more other variables.

Weighted Average

A method of computing a kind of arithmetic mean of a set of numbers in which some elements of the set carry more importance (weight) than others. Example: Grades are often computed using a weighted average. Suppose that homework counts 10%, quizzes 20%, and tests 70%.

Rational Expression

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

Direct Variation

A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first.

Inverse Variation

A relationship between two variables in which the product is a constant. When one variable increases the other decreases in proportion so that the product is unchanged.

Oblique Asymptote

A slant (oblique) asymptote occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator. To find the slant asymptote you must divide the numerator by the denominator using either long division or synthetic division.

Hyperbola

A special arch-shaped curve that follows this rule: For any point, the distances: • from that point to a fixed point (the focus), and • from that point to a fixed straight line (the directrix) are always in the same ratio. It is one of the "Conic Sections"

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

Horizontal asymptotes are horizontal lines that the graph of the function approaches as x. As the name indicate they are parallel to the x-axis.

Point Discontinuity

Points of discontinuity, also called removable discontinuities, are moments within a function that are undefined and appear as a break or hole in a graph. A point of discontinuity is created when a function is presented as a fraction and an inputted variable creates a denominator equal to zero.

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.

Reciprocal Function

The reciprocal function is a function defined on the set of nonzero reals, that sends every real number to its reciprocal, i.e., its multiplicative inverse.

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

Rational Function

a rational function is 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.

Rational Equation

an equation with radicals that have variables in the radicands.

Rational Inequality

an inequality that has a variable in the radicand.