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Rational Functions Assignment Help

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In the case of one variable, x, a function is called a rational function if and only if it can be written in the form

  • f(x) = P(x) / Q(x)

where P and Q are polynomial functions in x and Q is not the zero polynomial. The domain of f is the set of all points x for which the denominator Q(x) is not zero, where one assumes that the fraction is written in its lower degree terms, that is, P and Q have several factors of the positive degree.

Every polynomial function is a rational function with Q(x)=1. A function that cannot be written in this form (for example, f(x) = sin (x) ) is not a rational function (but the adjective "irrational" is not generally used for functions, but only for numbers).

An expression of the form P(x) / Q(x) is called a rational expression. The x need not be a variable. In abstract algebra the x is called an indeterminate.

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