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Unformatted text preview: Create assignment, 57950, Final 1, Dec 03 at 4:29 pm 1 This printout should have 109 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. CalC1b05 47:02, calculus3, multiple choice, > 1 min, wordingvariable. 001 Sketch the graph of the function f ( x ) = m ( x 3) + 4 for m = 1 , , 1. 1. 4 8 4 4 8 4 x y cor rect 2. 4 8 4 4 8 4 x y 3. 4 8 4 4 8 4 x y 4. 4 8 4 4 8 4 x y 5. 4 8 4 4 8 4 x y Explanation: Since each function f is linear, its graph will be a straight line. Furthermore, these lines will pass through (3,4) and have respective slope m = 1 , , 1. Consequently, the three graphs are given by Create assignment, 57950, Final 1, Dec 03 at 4:29 pm 2 4 8 4 4 8 4 x y CalC1c27 47:02, calculus3, multiple choice, > 1 min, wordingvariable. 002 Which one of the following is the graph of the function f ( x ) = sin  3 x  ? 1. 1 1 1 2 3 1 2 3 correct 2. 1 1 1 2 3 1 2 3 3. 1 1 1 2 3 1 2 3 4. 1 1 1 2 3 1 2 3 5. 1 1 1 2 3 1 2 3 Explanation: Note: The first full cycle of the sin(3 x ) function occurs when 3 x = 2 π ; i.e. , when x = 2 π 3 = 2 . 0944. Now the graph of the function f ( x ) = sin3 x, without the absolute value, is Create assignment, 57950, Final 1, Dec 03 at 4:29 pm 3 1 1 1 2 3 1 2 3 However, because  x  =  x  ,  x  = x ( x ≥ 0) , the function f ( x ) = sin  3 x  is an even function ( f ( x ) = f ( x )), so the graph to the left of the yaxis is the mirror image of the graph of sin3 x to the right of the yaxis. Consequently, the graph of f is: 1 1 1 2 3 1 2 3 CalC1a26s 47:02, calculus3, multiple choice, > 1 min, normal. 003 Find the natural domain of the function g ( u ) = √ u √ 7 u. 1. nat. domain = [0 , 7] correct 2. nat. domain = (0 , 7) 3. nat. domain = [0 , ∞ ) 4. nat. domain = (0 , 7] 5. nat. domain = [0 , 7) Explanation: The natural domain of g consists of all val ues of u for which both of the functions g 1 ( u ) = √ u, g 2 ( u ) = √ 7 u are defined. But g 1 is defined for all u ≥ 0, while g 2 is defined for all u ≤ 7. Consequently, natural domain = [0 , 7] . CalC1a35a 47:02, calculus3, multiple choice, > 1 min, wordingvariable. 004 Which function has 1 2 3 4 5 6 1 2 3 4 5 as its graph on [ 1 , 7]? 1. f ( x ) = 3 2 + 1 x 2 + 1  x 2  correct 2. f ( x ) = 3 2 1 x 2 1  x 2  3. f ( x ) = 1 x 2 + 1  x 2  3 2 4. f ( x ) = 3 2 + 1 x 2 1  x 2  Create assignment, 57950, Final 1, Dec 03 at 4:29 pm 4 5. f ( x ) = 3 2 1 x 2 + 1  x 2  Explanation: Since  x 2  = ‰ x 2 , x ≥ 2, 2 x, x < 2, we see that 1 x 2 + 1  x 2  = 2 x 2 , x > 2, , x < 2 ....
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This note was uploaded on 02/28/2010 for the course M 56200 taught by Professor Radin during the Fall '09 term at University of Texas.
 Fall '09
 RAdin

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