Math_41Exam_1_Part_2_key_-1

# Math_41Exam_1_Part_2_key_-1 - 3 9 g x x =(iii 2 5 g x x...

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Math 41 Exam 1 (Part 2) Name______________________________________________ Show your work! Answers without supporting work will receive no credit. Please circle your final answers! 1. [5] Approximate, to the nearest hundredth, any relative maximums and minimums of 3 2 ( ) 4 1 f x x x = - - , and find the intervals where the function is increasing and decreasing. 2. [4] Determine whether the following equations represent y as a function of x . Explain. (a) 5 x y = - + (b) 2 3 x y + = 3. [6] Determine (either graphically or algebraically) whether the function 3 ( ) 8 f x x = + has an inverse function, and if so, find the inverse function algebraically. 4. [8] For each of the following functions, (a) identify the parent function f , and (b) describe the sequence of transformations from f to g . (i) 2 ( ) ( 10) 5 g x x = - + + (ii) ( )

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Unformatted text preview: 3 9 g x x = + + (iii) ( ) 2 5 g x x =-(iv) 3 ( ) 3( 1) g x x =-5. [4] Write the slope-intercept form of the equation of the line that passes through the points (-1,-7), (1,-3). 6. [4] Algebraically determine whether the function 3 ( ) 5 h x x =-is even, odd, or neither. 7. [8] Use the functions 2 ( ) f x x = and ( ) 2 g x x =-to find the specified function and its domain. (a) ( )( ) f g x-(b) ( / )( ) f g x (c) ( )( ) f g x o (d) ( )( ) g f x o 8. [6] Find the difference quotient, ( ) ( ) , f x h f x h h +-for 2 ( ) 4 2 f x x x = +-. 9. [5] Find the domain and range of the function 2 ( ) 1 g x x = + . Extra Credit (5 points): Find two functions, f and g such that ( )( ) ( ) f g x h x = o , if 2 3 ( ) ( 2) h x x = + ....
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Math_41Exam_1_Part_2_key_-1 - 3 9 g x x =(iii 2 5 g x x...

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