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Sec-56 - Math 1300 Rational Functions Definition A rational...

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Math 1300 Section 5.6 Notes 1 Rational Functions Definition : A rational function is a function that contains a rational expression. Working with rational functions Rational functions and rational expressions are very similar, except rational functions are rational expressions that have been named. Examples: f ( x ) = 23 17 2 3 - + x x , g ( x ) = 1 2 1 2 - - x x x , h ( x ) = 10 11 8 2 2 2 + - - - x x x x Domain of a Rational Function (revisited): Remember: The domain of a rational function is all real numbers except where the denominator equals zero. To find the domain of a rational function, set the denominator not equal to zero and solve. Then write your answer in interval notation. Examples: 1. Find the domain of f ( x ) = 5 2 3 + - x x . To find the domain, set the denominator, 2 x + 5 0 and solve for x . Solve for x : 2 x + 5 0 2 x -5 x -5/2 Domain: (- , -5/2) (-5/2, ) 2. Find the domain of f ( x ) = 1 2 1 2 - - x x x . To find the domain, set the denominator, x 2 – 2 x + 1 0 and solve for x . x 2 – 2 x + 1 0 Factor: ( x – 1) 2 0 Zero-Product Property: x – 1 0 Solve for x : x 1 Domain: (- , 1) (1, ) 3. Find the domain of f ( x ) = 3 5 2 5 7 2 - - + x x x . To find the domain, set the denominator, 2 x 2 – 5 x – 3 0 and solve for x . 2 x 2 – 5 x – 3 0 Factor: (2 x + 1)( x – 3) 0 Zero-Product Property: 2 x + 1 0 and x – 3 0 Solve for x : x -½ and x 3 Domain: (- , -½) (-½, 3) (3, )
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Math 1300 Section 5.6 Notes 2 Vertical Asymptotes Above, we used the denominator to find the domain of a rational function.
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