This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Villarreal, Natalie Homework 1 Due: Sep 7 2007, 3:00 am Inst: Louiza Fouli 1 This printout should have 21 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. Yes, Homework 1 is due AFTER Homework 2. 001 (part 1 of 1) 10 points Rationalize the numerator of x + 5 x 3 x . 1. 8 x ( x + 5 x 3) 2. 8 x ( x + 5 + x 3) correct 3. 2 x x + 5 + x 3 4. 2 x ( x + 5 + x 3) 5. 8 x x + 5 x 3 Explanation: By the difference of squares, ( x + 5 x 3)( x + 5 + x 3) = ( x + 5) 2 ( x 3) 2 = 8 . Thus, after multiplying both the numerator and the denominator in the given expression by x + 5 + x 3 , we obtain 8 x ( x + 5 + x 3) . keywords: rationalization numerator, 002 (part 1 of 1) 10 points Simplify the expression f ( x ) = 4 + 4 x 2 3 + 9 x x 2 4 as much as possible. 1. f ( x ) = x 2 2 x 4 2. f ( x ) = 4 3 x 2 x + 4 3. f ( x ) = 4 3 x + 2 x + 4 correct 4. f ( x ) = x 2 x 4 5. f ( x ) = x + 2 x 4 6. f ( x ) = 4 3 x + 2 2 x + 4 Explanation: After bringing the numerator to a common denominator it becomes 4 x 8 + 4 x 2 = 4 x 4 x 2 . Similarly, after bringing the denominator to a common denominator and factoring it be comes 3 x 2 12 + 9 x x 2 4 = 3( x 1)( x + 4) x 2 4 . Consequently, f ( x ) = 4 + 4 x 2 3 + 9 x x 2 4 = 4 x 4 3( x 1)( x + 4) x 2 4 x 2 . On the other hand, x 2 4 = ( x + 2)( x 2) . Thus, finally, we see that f ( x ) = 4 3 x + 2 x + 4 . Villarreal, Natalie Homework 1 Due: Sep 7 2007, 3:00 am Inst: Louiza Fouli 2 keywords: 003 (part 1 of 1) 10 points Find the solution set of the inequality x 2 x 6 < x + 3 x + 2 . 1.  14 3 , 2 [ 6 , 2.  , 14 3 i [  2 , 6 3.  , 14 3 [  2 , 6 correct 4. h 14 3 , 2 [ 6 , 5.  , 14 3 [ h 2 , 6 Explanation: To begin we need to arrange that all the terms are on one side of the inequality. Thus the inequality becomes x 2 x 6 x + 3 x + 2 < , which in turn becomes ( ) 3 x + 14 ( x + 2)( x 6) < after the right hand side is brought to a com mon denominator. Now the right hand side changes sign at the zeros of its numerator and denominator, i.e. , at x = 14 3 , 6 , 2, and the sign chart 14 3 2 6 + + determines which sign it takes in a given in terval. Thus the solution set of ( ) is the union  , 14 3 [  2 , 6 . keywords: 004 (part 1 of 1) 10 points The straight line is parallel to y + 3 x = 1 and passes through the point P (4 , 2). Find its xintercept....
View
Full
Document
 Fall '09
 Gualdani

Click to edit the document details