Kizlik S. Quickstudy for Calculus 2007

Textbook in PDF format Use this QuickStudy* booklet to make the most of your studying time. All equations are set in boldface type for easy reference. Definitions Function: A correspondence that assigns one value (output) to each member of a given set. The given set of inputs is called the domain. The set of outputs is called the range. One-variable calculus deals with real-valued functions whose domain is a set of real numbers. If a domain is not specified, it is assumed to include all inputs for which there is a real number output. @ Notation: If a function is named f, then f(x) denotes its value at x, or “fevaluated at x.” If a function gives a quantity y in terms of a variable quantity x, then x is called the independent variable and y the dependent variable. Given a function by an equation such as y = x’, one may think of y as shorthand for the function’s expression. The notation x|—>x? (“x maps to x””) is another way to refer to the function. The expression f(x) for a function at an arbitrary input x often stands in for the function itself. Graph: The graph of a function f is the set of ordered pairs (x, f(x)), presented visually on a Cartesian coordinate system. @ The vertical line test states that a curve is the graph of a function if every vertical line intersects the curve at most once. @ An equation y = f(x) often refers to the set of points (x, y) satisfying the equation, in this case the graph of the function f, The zeros of a function are the inputs x for which f(x) = 0, and they are the x-intercepts of the graph. Even & Odd: A function fis even if f(-x) = f(x) and odd if f(—x) = —f(x). Most are neither

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