Algebra.Com's Answer #99748 by solver91311(24713)![\"\"](\"/images/stars/stars-13.gif\")  
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if f is a function, f(x) is the value of the function at x. The domain of the function is the set of all possible values for which the function is defined.\r
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document.write( "For example (note that the following presumes that the functions are mapped to the real numbers):\r
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document.write( " . f is defined for all real values of x. Hence the domain is all reals.\r
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document.write( " . if  , then the denominator is zero, so g is not defined for , therefore the domain is the set of all x such that x is a real number and x is not equal to 2.\r
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document.write( " . if  then the quantity under the radical is negative, meaning h is not defined in the reals. Therefore the domain of the function is the set of all x such that x is real and  .\r
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document.write( "The range is the set of all possible values of the function over the domain of the function.\r
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document.write( "Using the above examples:\r
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document.write( ". This function is continuous over the reals and as x increases without bound, f(x) increases without bound. The range is all reals.\r
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document.write( ". For any real value of x,  , g(x) maps to a real number, and for any value of g(x), an x exists that will map to that g(x). The range is all reals.\r
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document.write( " . The notational convention is that the radical means the positive square root. If it were taken to mean either the positive or negative square root, h would not be a function because for all values of x in the domain of h except  , h(x) could take on two different values, thus violating the definition of a function. Therefore, the range of this function is all non-negative reals (all positive reals and zero). Expressed as a set: the set of all y such that y is real and  .\r
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document.write( " where  is the number of gallons of capacity in your automobile gas tank and  is the cost per gallon at the pump. The function results in the total cost for a tank of gasoline. \n" );
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