Properties of Rational Functions
Rational Functions – A rational function is defined as the function which can be expressed as a ratio of two given polynomials. The polynomial functions can have any highest exponent and it is written in the general form as:
A rational function is of the general form:
- f(x) = (x+ 2) / (x2-3x+ 2)
- g(x) = (3x+7) / ( 5x-8)
- h(x) = (x3 – 2x2 + 10) / ( x – 1)
Domain of a rational function is not all real numbers, because of the fact that there is a function in the denominator.
If the value in the denominator of a function = 0, then the function goes to infinity and we don’t want that!
Example:Find the domain and simplify: f(x) = (x2 – x + 12) / (x – 4)
Domain: x – 4 = 0 -> x = 4
So, domain: (-infinity, 4) U (4, infinity)
Simplification by factoring the numerator: f(x) = (x-4)(x+3) / (x-4)
f(x) = (x+3)ç (reduced form)
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