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A "function" is a special kind of relationship between two quantities (variables) where the dependent variable is unique with respect to the independent variable. The collection of all the independent variables is called the "domain" and the collection of all the dependent variables is called the "range". We use f(x) notation (instead of y) to represent the dependent variable. The function could also be named g(x), h(x), j(x), or whatever. Consider...f(x) = 3x + 2. This relationship can be used to complete a table of data points as follows:
f(x) values are determined by simple substitution of the x values into the given function and evaluating using all rules for exponents and order of operations........... f(3) = 3(3) + 2 = 9 + 2 = 11 This is an example of a "Linear" Function since the resulting data points graph into a line. Other types of functions are computed using the same subsitution procedure. Try.....f(x) = 3x2 - 24 and find the value of f(4). Then find f(-3). f (4) = 3 (42 - 24 = 3(16) - 24 = 48-24 = 24 f(-3) = 3(-32 - 24 = 3(9) - 24 = 27 - 24 = 3 When trying to determine the quadratic equation for given data points, a minimum of three (3) points are needed. As we continue with our study of functions, we will encounter some cases where restrictions may exist for either the domain, range, or both. The previous examples do not have any restrictions. An example of a function which will have a restriction is f(x) = 1/x. Since negative numbers is undefined and since division by 0 is undefined, the values for x (or the domain) is limited to only positive real numbers. Hence, the range is also composed of only positive real numbers. If using a graphing utility to evaluate functions, follow this procedure: type function using Y =, press Enter, press Table (second graph) to view all data points, scroll to find desired "x" value and read "f(x)" or "y" value from the table. For non integer x values consult your instructor for directions to customize the table using table set button. After completing the lessons on Math Models and Functions, a student should be able to:
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