# Domain and Range of a Function - 10/30/2014 Domain and...

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10/30/2014Domain and Range of a Function1/8interactive mathematicsLearn math by playing with it!Home»Functions and Graphs» 4a. Domain and Range of a FunctionDomain and Range of a FunctionDomainThedomainof a function is the complete set of possible values of the independent variable.In plain English, this definition means:The domain is the set of all possiblex-values which will make the function "work", and will outputrealy-values.Remember:The denominator (bottom) of a fractioncannot be zeroThe number under a square root signmust be positivein this workExample 1aHere is the graph ofy:The domain of this function isx, sincexcannot be less than. To see why, try out some numbers lessthan(likeor) and some more than(likeor) in your calculator. The only ones that "work"and give us an answer are the ones greater than or equal to. This will make the number under the square rootpositive.Notes:1. The enclosed (colored-in) circle on the point. This indicates that the domain "starts" at this point.2. We saw how to draw similar graphs in section 4,Graph of a Function. For a more advanced discussion,see alsoHow to draw y^2 = x − 2.x
10/30/2014Domain and Range of a Function2/8RangeTherangeof a function is the complete set of all possibleresulting valuesof the dependent variable (y,usually),after we have substituted the domain.In plain English, the definition means:The range is the resultingy-values we get after substituting all the possiblex-values.TipsSubstitute differentx-values into the expression foryto see what is happening. (Ask yourself: Isyalwayspositive? Always negative? Or maybe not equal to certain values?)Make sure you look forminimumandmaximumvalues ofy.Drawasketch!In math, it's very true that a picture is worth a thousand words.

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Continuous function