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MAC1140E3sum2009 - MAC 1140 SUMMER B 2009 EXAM III...

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MAC 1140 SUMMER B 2009 EXAM III Disclaimer: This review is by no means complete. Please study the homework as well as the lecture notes. These questions should be attempted only after you have completed all the homework assignments. You may need a calculator to solve a couple of these problems, however the exam questions will be choosen in such a way that you do not need a calculator. 1. (Section 1.6) Know the parent functions on page 70. (a) Graph the function and find the domain and range for f ( x ) = 2 - 2 x if x < - 1 4 if - 1 < x < 2 - x 2 if x 2 2. (Section 1.7) Transformations of Functions (a) Sketch the following functions by using transformations of parent functions: f ( x ) = - 3( x - 2) 3 - 4 g ( x ) = 1 2 - x - 3 h ( x ) = - 1 3 | x | - 1 (b) Using the graphs from part (a) find the domain and range. 3. (Section 1.8) Combinations of Functions (a) Let f ( x ) = x - 1 and g ( x ) = 4 - x 2 . Find following functions with their domain: ( f - g )( x ) f g ( x ) ( fg )( x ) ( f + g )( x ) (b) Find the functions f and g such that ( f g )( x ) = 1 + x 2 x 2 (c) Let f ( x ) = 3 - x and g ( x ) = 1 x 2 . Find the following functions with their domain: ( f g )( x ) ( g f )( x ) ( f f )( x ) ( g g )( x ) ( f f f )( x ) (d) If f and g are odd functions, show that the composite function f g is also odd.
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