1 - Nguyen(ln4328 – HW#1 – treisman –(54540 1 This...

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Unformatted text preview: 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 ≤ 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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This note was uploaded on 11/10/2010 for the course M 408c taught by Professor Mcadam during the Fall '06 term at University of Texas.

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1 - Nguyen(ln4328 – HW#1 – treisman –(54540 1 This...

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