calatogue_of_functions

# calatogue_of_functions - Catalogue of Important Functions...

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Catalogue of Important Functions We list several important functions, draw their graphs and indicate domains and ranges. In the forthcoming sections we will study their properties and use them in various applications. As well, we will add more functions to our catalogue. (1) The function f ( x ) = c where c is a real number is a constant function . It assigns the same number c to all values of the independent variable x . Its domain is the set of real numbers, and the range consists of the single value c . The graph in Figure 1.2.D shows the constant function f ( x ) = 2 . x y O f ( x ) = 2 2 Figure 1.2.D Constant function (2) The function f ( x ) = mx + b , where m and b are real numbers, is called a linear function . Its graph is a line of slope m and y -intercept b . When m 0 , then both domain and range consist of all real numbers. If m = 0 , the line is horizontal, so it represents a constant function f ( x ) = b . The special case y = x is a line of slope 1 through the origin, see Figure 1.2.E. Sometimes we calculate the linear function from the

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calatogue_of_functions - Catalogue of Important Functions...

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