Graphing-Rational-Functions - Graphing Rational Functions A...

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Graphing Rational Functions A rational function is defined here as a function that is equal to a ratio of two polynomials p(x)/q(x) such that the degree of q(x) is at least 1. Examples: is a rational function since it is a ratio of two polynomials with degree in the denominator greater than or equal to 1. is not a rational function since the degree of the denominator is not greater than or equal to 1. is not a rational function since the numerator is not a polynomial. Reduced Rational Functions A reduced rational function is one where there are no factors common to the numerator and denominator. For example, y = (x –1)/(x 2 – 4) is in reduced form since there is no factor of (x-1) in the denominator. Example of Non-Reduced Form: y = (x 2 – 4)/(x – 2) is in non-reduced form since it may be written as y =[(x + 2)(x-2)]/(x-2) which may be reduced to y = x + 2 after canceling common factors of (x-2). So the equation simplifies to a linear equation! However, since x=2 results in division by zero in the original function, we are missing the point at x=2. The graphs of both y=x+2 and our rational function are shown below. TIP: Always simplify a rational function first, if possible. And remember to exclude any values of x from the domain that result in division by zero.
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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes The Simplest Rational Function: y = 1/x If you graph the simplest rational function y = 1/x, you get the solution points and graph shown (in blue) below:
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This note was uploaded on 11/30/2010 for the course CIIVIL WNG 33155 taught by Professor Y.bahie during the Spring '10 term at The British University in Egypt.

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Graphing-Rational-Functions - Graphing Rational Functions A...

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