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110quiz1solutions

110quiz1solutions - ning short of time he drives faster now...

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Math 110 Quiz 1 August 31, 2006 Name: 1. Use the function Q ( x ) = 2 x 2 - 3 to simplify each expression: (a) Q ( x + 3) (b) Q ( x ) + Q (3) (c) Q ( x ) + 3 (d) x + Q (3). Solutions: (a) Q ( x + 3) = 2( x + 3) 2 - 3 = 2( x 2 + 6 x + 9) - 3 = 2 x 2 + 12 x + 15 (b) Q ( x ) + Q (3) = 2 x 2 - 3 + 2(3) 2 - 3 = 2 x 2 - 3 + 18 - 3 = 2 x 2 + 12 (c) Q ( x ) + 3 = 2 x 2 - 3 + 3 = 2 x 2 (d) x + Q (3) = x + 2(3) 2 - 3 = x + 18 - 3 = x + 15 2. Sketch a graph of the following piece-wise function. Be sure to label the axes and important points. g ( y ) = - 2 y, y < 3; y 2 , y 3 1
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3. Find the domain and range of the function w ( x ) from the graph below. Solution: Domain= [ - 3 , - 1) ( - 1 , ) Range= ( -∞ , 2] 2
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4. From the following scenerio, sketch a qualitative graph for Neil’s distance from home as a function of time: Neil leaves home in his car, bound for class. Since he is early, he starts off slowly. Suddenly, he remembers that his homework is at home on the table, so he turns around and returns home to get his homework. Run-
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Unformatted text preview: ning short of time, he drives faster now; arriving at school just in time for class. Solution: In the figure below, A represents the time Neil realizes he forgot his homework and turns around, B repre-sents the time he returns home (where is distance from home is zero), and C represents his entrance into class, which is just on time. 3 5. Let G ( x ) = 2 x ( x 2-4 x + 3) . (a) Draw a complete graph of G ( x ). (b) Approximate graphically (to the nearest 0.001) the zeros of G ( x ). Solution: (b)Using the zoom and trace functions on a standard graphing calculator, we see that x = 1 . 000 and x = 3 . 000 are zeros. (a) 4...
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