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Elementary and Intermediate Algebra
Mark Dugopolski, Southeastern Louisiana University

Functions

Key Terms


absolute value function  A function of the form f(x) = |x|.
average rate of change  The ratio of the change in y to the change in x.
constant function  A function of the form f(x) = k for some constant k.
direct variation  The relationship between two quantities, x and y, such that y = kz, where k is a constant.
function  A set of ordered pairs of real numbers in which no two have the same first and different second coordinates.
horizontal line test  A visual method for determining whether a function is one-to-one.
inverse of the function f  A function in which the ordered pairs of f are reversed.
inverse variation  The relationship between two quantities, x and y, such that y = k/x, where k is a constant.
joint variation  The relationship between three quantities, x, y, and z, such that z = kxy.
one-to-one function  A function in which no two ordered pairs have the same second coordinate and different first coordinates.
relation  Any set of ordered pairs.
sum of f and g  The function (f + g)(x) where (f + g)(x) = f(x) + g(x).
synthetic division  A quick method for dividing by x - c.
varies directly  A function of the form y = kx where k is a non-zero constant.
varies inversely  A function of the form y = k/x where k is a non-zero constant.
vertical line test  If there is a vertical line that crosses a graph more than once, then the graph is not the graph of a function.
zero of a function  A number a such that f(a) = 0.