Question 821952: In a rational function, explain domain and range. Explain how the denominator influences domain and range.
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! For all functions, not just rational ones, the domain is the set of all possible inputs to the function. And the range is the set of all possible outputs from the function.
Since division by zero is not allowed, domains of rational functions must be restricted to eliminate any inputs which would make a denominator zero. For example, for the function f(x) = 1/(x-5), the domain would have to exclude 5 since an input of 5 would make the denominator zero. (The domain would be all real numbers except 5.) But for g(x) = 1/(x^2+1) there is no reason to exclude any numbers since the denominator can never be zero no matter what the input is.
The denominator by itself has no effect on the range.
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