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Unformatted text preview: myers (nmm698) HW01 Hamrick (54868) 1 This printout should have 21 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Simplify the expression f ( x ) = 3 + 9 x 2 1 3 parenleftBig x x 2 4 parenrightBig as much as possible. 1. f ( x ) = 3( x 2) x 4 2. f ( x ) = x 2 x + 4 3. f ( x ) = 3( x + 2) 2 x 4 4. f ( x ) = 3( x + 2) x 4 correct 5. f ( x ) = x + 2 x + 4 6. f ( x ) = x 2 2 x + 4 Explanation: After bringing the numerator to a common denominator it becomes 3 x 6 + 9 x 2 = 3 x + 3 x 2 . Similarly, after bringing the denominator to a common denominator and factoring it be comes x 2 4 3 x x 2 4 = ( x + 1)( x 4) x 2 4 . Consequently, f ( x ) = 3 + 9 x 2 1 3 parenleftBig x x 2 4 parenrightBig = 3 x + 3 ( x + 1)( x 4) parenleftBig x 2 4 x 2 parenrightBig . On the other hand, x 2 4 = ( x + 2)( x 2) . Thus, finally, we see that f ( x ) = 3( x + 2) x 4 . 002 10.0 points Let f be the quadratic function defined by f ( x ) = 2 x 2 12 x 14 . Use completing the square to find h so that f ( x ) = 2( x h ) 2 + k for some value of k . 1. h = 3 correct 2. h = 6 3. h = 3 4. h = 6 5. h = 12 Explanation: Completing the square gives f ( x ) = 2 x 2 12 x 14 = 2( x 2 6 x 7) = 2( x 2 6 x + 9 7 9) . Thus f ( x ) = 2( x 2 6 x + 9) 32 = 2( x 3) 2 32 . Consequently, h = 3 . myers (nmm698) HW01 Hamrick (54868) 2 003 10.0 points Which, if any, of the following statements are true when a, b are real numbers? A. For all positive a and b , a + b = radicalBig a + 2 ab + b . B. For all a and b , radicalBig ( a + b ) 2 = a + b . C. For all positive a and b , a b a + b = a b . 1. A and C only correct 2. A and B only 3. B and C only 4. A only 5. C only 6. B only 7. all of them 8. none of them Explanation: A. TRUE: by the known product, ( x + y ) 2 = x 2 + 2 xy + y 2 . On the other hand, radicalBig ( x + y ) 2 =  x + y  , so if x + y > 0, x + y = radicalbig x 2 + 2 xy + y 2 . But if a, b are positive we can set x = a and y = b . The result follows since x and y are then positive. B. FALSE: radicalBig ( x + y ) 2 =  x + y  , and since radicalbig ( ) is always nonnegative, the right hand side has to be nonnegative. But if a, b can be positive or negative, an absolute value sign is then needed on the right. C. TRUE: by the known difference of squares factorization, x 2 y 2 = ( x y )( x + y ) . But if a, b are positive we can set x = a and y = b . The result follows after division....
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 Fall '08
 schultz

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