UFCalcSet4 - Exercises UF Calculus Set 4 1 Describe in two...

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Exercises UF Calculus Set 4 1. Describe, in two steps, how to transform the graph of f ( x ) into the graphs of the functions: (a) f (2 - x ) (b) 2 - f ( x ) What graphs do you obtain if you reverse the two steps in each case? are they the same? 2. Use the displayed graph of f ( x ) to draw the graphs of the functions below (a) 1 + f ( x + 2) (b) 2 f (3 x ) (c) 2 f (3( x - 2)) + 1 (d) | f ( x ) | 3. Starting with the graph of y = x , the graph of y = 1 /x , and the graph of y = 1 - x 2 (the upper unit semicircle), sketch the graphs of each of the following functions: (a) y = 1 x + 1 (b) y = x 1 - x (c) y = 4 + x + 2 (d) y = - - x (e) y = 2 + p 1 - ( x - 1) 2 (f) y = 2 r 1 - ( x 3 ) 2 4. Given the functions f, g, h , write a simplified formula for the new functions listed. Include the domain of each. f ( x ) = x + 1 g ( x ) = 1 x h ( x ) = x 2 (a) f + g (b) f · g · h (c) h g (d) f · g x + 1 (e) f h (f) h f (g) f g (h) g f
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5. Express each function as f g where g ( x ) = 1 + x 2 and f ( u ) = Au b for some constants A, b . (a) 2(1 + x 2 ) 10 (b) 5 3 1 + x 2 2 6. During the course of an experiment, the following data is collected for the functions
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