Math_41_Exam_1Part_1_key_

Math_41_Exam_1Part_1_key_ - that 2 2 x f x x g x = =(a...

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Math 41 Exam 1 Name___________________________________________________ Show your work! Answers without supporting work will receive no credit. Please circle your final answers! 1. (6) Compare the graph of 3 1 4 ( ) ( 2) h x x = + with the graph of 3 ( ) f x x = . Describe the transformation. 2. (9) Find (a) ( )( ) f g x + , (b) ( )( ) f g x - , (c) ( )( ) fg x , (d) ( / )( ) f g x , given 2 3 1 1 ( ) , ( ) f x g x x x = = . Simplify!!! What is the domain of f/g ? 3. (6) Show that f and g are inverse functions algebraically . Use a graphing utility to graph f and g in the same viewing window, and draw the graph. Describe the relationship between the graphs. ( ) 4 f x x = - , 2 ( ) 4, 0 g x x x = + . 4. (6) Find the slope-intercept form of the equation of the line that passes through the points (4,3) and (-4,-4).

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5. (6) Determine the domains of (a) f , (b) g , (c) f g o , given 2 1 ( ) 2, ( ) 4 f x x g x x = + = - . 6. (6) Show that f and g are inverse functions (a) graphically and (b) numerically, given
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Unformatted text preview: that ( ) 2 , ( ) 2 x f x x g x = = . (a) Graphically (b) Numerically y 1 = y 1 = y 2 = y 2 = 7. (6) A company produces a toy for which the variable cost is \$12.30 per unit and the fixed costs are \$98,000. The toy sells for \$17.98. Let x be the number of units produced and sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost C as a function of the number of units produced. (b) Write the revenue R as a function of the number of units sold. (c) Write the profit P as a function of the number of units sold. (Note: P=R-C ). 8. (5) Use your calculator to approximate any relative minimum or maximum values of the function ( ) 4 g x x x =-. Round to the nearest hundredth....
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Math_41_Exam_1Part_1_key_ - that 2 2 x f x x g x = =(a...

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