HW01-solutions - snavely (ras3985) HW01 radin (55615) 1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: snavely (ras3985) HW01 radin (55615) 1 This print-out should have 24 questions. Multiple-choice 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 4 1 + 15 parenleftBig x x 2 16 parenrightBig as much as possible. 1. f ( x ) = 3( x 4) x + 16 2. f ( x ) = x + 4 x 16 3. f ( x ) = 3( x + 4) 2 x + 16 4. f ( x ) = 3( x + 4) x + 16 correct 5. f ( x ) = x 4 2 x 16 6. f ( x ) = x 4 x 16 Explanation: After bringing the numerator to a common denominator it becomes 3 x 12 + 9 x 4 = 3 x 3 x 4 . Similarly, after bringing the denominator to a common denominator and factoring it be- comes x 2 16 + 15 x x 2 16 = ( x 1)( x + 16) x 2 16 . Consequently, f ( x ) = 3 + 9 x 4 1 + 15 parenleftBig x x 2 16 parenrightBig = 3 x 3 ( x 1)( x + 16) parenleftBig x 2 16 x 4 parenrightBig . On the other hand, x 2 16 = ( x + 4)( x 4) . Thus, finally, we see that f ( x ) = 3( x + 4) x + 16 . 002 10.0 points Let f be the quadratic function defined by f ( x ) = 2 x 2 4 x 30 . Use completing the square to find h so that f ( x ) = 2( x h ) 2 + k for some value of k . 1. h = 2 2. h = 2 3. h = 1 4. h = 4 5. h = 1 correct Explanation: Completing the square gives f ( x ) = 2 x 2 4 x 30 = 2( x 2 2 x 15) = 2( x 2 2 x + 1 15 1) . Thus f ( x ) = 2( x 2 2 x + 1) 32 = 2( x 1) 2 32 . Consequently, h = 1 . snavely (ras3985) HW01 radin (55615) 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 = a + 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. none of them 2. B and C only 3. A and C only 4. C only 5. A and B only 6. B only correct 7. A only 8. all of them Explanation: A. FALSE: 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 , in which case a + b = radicalBig a + 2 ab + b , contrary to the assertion. B. TRUE: we know that radicalBig ( x + y ) 2 = | x + y | , and since radicalbig ( ) is always non-negative, the right hand side has to be non-negative. Thats why the absolute value sign is needed. C. FALSE: 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 . Thus, after division, a b a + b = a b , contrary to the assertion....
View Full Document

This note was uploaded on 02/19/2011 for the course MATH 408 K taught by Professor Clark,c.w./hoy,r.r during the Spring '08 term at University of Texas at Austin.

Page1 / 13

HW01-solutions - snavely (ras3985) HW01 radin (55615) 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online