1 - merino(aem2588 HW 1 chen(55405 This print-out should...

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Nguyen (ln4328) – HW #1 – treisman – (54540) 1 This print-out should have 14 questions. Multiple-choice 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 semi-circle 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 piecewise-defined 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 0 in order to eliminate the absolute values from the definition of f ( x ). Now the left hand side
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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 of f consists of the union ( −∞ , 7) ( 7 , ) .
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