X 4 3 2 1 1 2 3 y 4 4 2 9 4 3 1 1 a for what values

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x - 4 - 3 - 2 - 1 0 1 2 3 y - 4 4 - 2 9 4 3 1 - 1 (a) For what values of x is y = 4? (b) For what values of x is y = 5? (c) For what values of y is x = 0? (d) For what values of x is y 0? (e) What is the minimum value of y ? At what value of x does it occur? (f) What is the maximum value of y ? At what value of x does it occur? Solution: SOLUTION Referring to the table: (a) y = 4 at x = - 3 , 0. (b) There is no value for x where y = 5. (c) x = 0 at y = 4. (d) y 0 at x = - 4 , - 2 , 3. (e) The minimum value of y is - 4 . This occurs at x = - 4. (f) The maximum value of y is 9 . This occurs at x = - 1. Answer(s) submitted: -3,0 N 4 -4,-2,3 -4 -4 9 -1 (correct) Correct Answers: -3, 0 none 4 -4, -2, 3 -4 -4 9 -1 30. (1 point) Find f ( 9 ) , f ( - 8 ) , f ( π ) , and f ( - 8 . 1 ) for : f ( x ) = x + 8 if x > 8 7 if x 8 You may keep radicals in any answers where appropriate. Use pi to represent π . f ( 9 ) = f ( - 8 ) = f ( π ) = f ( - 8 . 1 ) = Solution: SOLUTION To evaluate a function at a specific value of the input variable x , replace all instances of the variable x with the input value and evaluate the resulting expression. In the case of a piece- wise function such as this one, you must first determine which ”branch” of the function to use, based upon the definition of the function and the input value of x . For f ( 9 ) , 9 > 8 and so the upper portion of the definition is used. Therefore, f ( 9 ) = 9 + 8 = 17 . For f ( - 8 ) , - 8 < 8 and so the lower portion of the definition is used. Therefore, f ( - 8 ) = 7 . For f ( π ) , π < 8 and so the lower portion of the definition is used. Therefore, f ( π ) = 7 . For f ( - 8 . 1 ) , - 8 . 1 < 8 and so the lower portion of the definition is used. Therefore, f ( - 8 . 1 ) = 7 . Answer(s) submitted: sqrt17 7 7 7 (correct) Correct Answers: 4.12311 7 7 7 31. (1 point) Are the following statements true or false? ? 1. The set of all x ’s that are in the domain of g and in the domain of f and where f ( x ) 6 = 0 correctly describes the domain of g f ( x ) . ? 2. If x is in the domain of f g , then x is in the domain of ( f + g )( x ) . ? 3. For any relation f , it must be that f ( c · x ) = c · f ( x ) as long as c is a constant. 8
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? 4. The set of all x ’s that are in the domain of g and where g ( x ) is in the domain of f correctly describes the do- main of f ( g ( x )) . ? 5. If f ( x ) = 5, then f ( a + h ) = 5. ? 6. If x is in the domain of g , then x is in the domain of ( f + g )( x ) . Answer(s) submitted: True True False True True False (correct) Correct Answers: TRUE TRUE FALSE TRUE TRUE FALSE 32. (1 point) The table below A = f ( d ) , the amount of money A (in billions of dollars) in bills of denomination d circulating in US currency in 2005. For example according to the table values below there were $60.2 billion worth of $50 bills in circulation. Denomination (value of bill) 1 5 10 20 50 100 Dollar Value in Circulation 8.4 9.7 14.8 110.1 60.2 524.5 a) Find f ( 10 ) = b) Using your answer in (a), what was the total number of $10 bills (not amount of money) in circulation in 2005?
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  • Fall '13
  • DrSulllivan
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