Sec-56 - Math 1300 Section 5.6 Notes 1 Rational Functions Definition A rational function is a function that contains a rational expression Working

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Unformatted text preview: 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, ∞ ) Math 1300 Section 5.6 Notes 2 Vertical Asymptotes Above, we used the denominator to find the domain of a rational function. Above, we used the denominator to find the domain of a rational function....
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This note was uploaded on 02/22/2012 for the course MATH 1300 taught by Professor Staff during the Spring '08 term at University of Houston.

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Sec-56 - Math 1300 Section 5.6 Notes 1 Rational Functions Definition A rational function is a function that contains a rational expression Working

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