FinalF10_Solns

# FinalF10_Solns - Math 105 Final Exam Name EXAM SOLUTIONS...

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Math 105 / Final (December 17, 2010) page 2 1 . [10 points] For each statement below, circle True if the statement is always true. Otherwise, circle False . You do not have to show any work for your answers. a . [2 points] If f is an invertible function and f (5) = 2, then f - 1 (5) = 1 2 . True False b . [2 points] If h is an invertible function, then the domain of h - 1 is the range of h . True False c . [2 points] If a radioactive substance decays 25% every year, then its half-life is two years. True False d . [2 points] The function f ( x ) = e 2 x + 1 is a linear function. True False e . [2 points] The line y = 4 is a horizontal asymptote of the function y = f ( x ) = 3 - 5 x 2 + 4 x x + 2 . True False
Math 105 / Final (December 17, 2010) page 3 2 . [10 points] a . [5 points] A portion of the graph of a power function q ( x ) is shown below. Find a formula for q ( x ). x (1 , 9) (3 , 1 3 ) y = q ( x ) y Solution: Because we are told q ( x ) is a power function, we know that q ( x ) = kx p for some constants k and p . Inserting the point (1 , 9) into the equation, we get 9 = k 1 p = k, so k = 9. Now using the second point, 1 3 = 9(3) p 1 27 = 3 p ln( 1 27 ) = p ln(3) So p = ln( 1 27 ) / ln(3) = - 3. Answer:

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FinalF10_Solns - Math 105 Final Exam Name EXAM SOLUTIONS...

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