1300_section5o6 - – 2 x 1 ≠ 0 and solve for x x 2 – 2...

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Math 1300 Section 5.6 Notes 1 5.6 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
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Unformatted text preview: – 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 Math 1300 Section 5.6 Notes 2 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, ∞ ) Examples: 1. Find the domain of: 2 1 ) ( + + = x x x f . ? ) 2 ( = f , ? ) ( = f 2. Find the domain of: x x x x f 5 1 ) ( 2 + + = . ? ) 1 ( = f , ? ) ( = f 3. Find the domain of: 100 ) ( 2-= x x x f . ? ) 1 ( = f , ? ) ( = f 4. Find the domain of: 6 5 4 ) ( 2-+ + = x x x x f . ? ) 1 ( = f , ? ) 2 ( =-f...
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1300_section5o6 - – 2 x 1 ≠ 0 and solve for x x 2 – 2...

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