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:

Examples: 

• 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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You can also Read our other blog Nonlinear Functions & Quadratic (Algebra)