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Unformatted text preview: Nguyen (ln4328) HW #1 treisman (54540) 1 This printout should have 14 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the domain and range of the function h ( x ) = radicalbig 25 x 2 . 1. domain = [ 5 , 5] , range = [0 , 5] cor rect 2. domain = [ 5 , 5] , range = [ 5 , 5] 3. domain = [0 , 5] , range = [5 , 5) 4. domain = ( , ) , range = [0 , ) 5. domain = ( 5 , 5) , range = (0 , 5) 6. domain = [0 , 5] , range = [0 , 5] Explanation: If we write y = radicalbig 25 x 2 , then x 2 + y 2 = 25 whose graph is a circle centered at the origin having radius 5. Thus the graph of h is the upper semicircle shown in 5 5 5 Consequently, h has domain = [ 5 , 5] , range = [0 , 5] . keywords: range, range of function 002 10.0 points Express the function f ( x ) = vextendsingle vextendsingle vextendsingle x 4 x + 7 vextendsingle vextendsingle vextendsingle as a piecewisedefined function by eliminating the absolute value signs. 1. f ( x ) = x 4 x + 7 , ( , 4) (7 , ) , 4 x x + 7 , ( 4 , 7) 2. f ( x ) = 4 x x + 7 , ( , 7) (4 , ) , x 4 x + 7 , ( 7 , 4] 3. f ( x ) = x 4 x + 7 , ( , 7) (4 , ) , 4 x x + 7 , [ 7 , 4] 4. f ( x ) = x 4 x + 7 , ( , 7) (4 , ) , 4 x x + 7 , ( 7 , 4] correct 5. f ( x ) = 4 x x + 7 , ( , 7) (4 , ) , x 4 x + 7 , [ 7 , 4] Explanation: Since  v  = braceleftbigg v, v 0, v, v < 0, we need to find the solution set of the inequal ity ( ) x 4 x + 7 in order to eliminate the absolute values from the definition of f ( x ). Now the left hand side Nguyen (ln4328) HW #1 treisman (54540) 2 of ( ) changes sign at x = 7 , 4, and the sign chart 7 4 + + determines which sign it takes. Thus f ( x ) = x 4 x + 7 , ( , 7) (4 , ) , 4 x x + 7 , ( 7 , 4] , the value x = 7 being excluded from the definition of f ( x ) because the natural domain...
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 Fall '06
 McAdam
 Calculus

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