Chpt. 8, Rational Functions Flashcards
inverse variation
A relation represented by an equation of the form xy = k, y = k/x, or x = k/y, all where k does not equal 0.
combined variation
A relation in which one variable varies with respect to two or more variables.
joint variation
A relation in which one variable varies directly to each of two or more variables.
combined variation types
z varies jointly with x and y: z = kxy
z varies jointly with x and y, and inversely with w: z = (kxy) / w
z varies directly with x and inversely with the product yw: z = kx/wy
reciprocal function
A function that belongs to the family whose parent function is f(x) = 1/x, where x does not equal zero. It can be written in the form f(x) = (a / (x -h)) +k, where neither a nor x equal zero.
branch
Used to refer to each piece of a discontinuous graph.
rational function
A function that can be written as f(x) = P(x) / Q(x), where both P(x) and Q(x) are polynomial functions. The domain of a rational function is all real numbers except those for which Q(x) = 0.
continuous graph
A graph that has no jumps, breaks, or holes.
discontinuous graph
A graph that has a jump, break, or hole.
point of discontinuity
The x-coordinate of a point where the graph of f(x) is not continuous.
removable discontinuity
A point of discontinuity, a, of function f that one can remove by redefining f at x = a. Doing so fills in the hole in the graph of f with the point (a, f(a)).
non-removable discontinuity
A point of discontinuity that is not removable. It represents a break in the graph of x where you cannot redefine f to make the graph continuous.
rational expression
The quotient of two polynomials.
simplest form of a rational expression
The form in which the numerator and denominator are polynomials that have no common divisor other than 1.
complex fraction
a rational expression that has a fraction in its numerator or denominator, or in both
