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Exercises-Review_Part_I

# Exercises-Review_Part_I - MA100 Fall 2010 PART 1...

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MA100, Fall 2010, PART 1: Precalculus Review Exercises [1] Find the equation of the line through (1 , 4) and slope - 3 . [2] Determine the domain of the functions: a) f ( x ) = x + 5 5 - 2 x + 1 x b) f ( x ) = ln(2 x - 7) c) f ( x ) = 6 1 - 5 x [3] Solve | x - 2 | ≥ 5 . [4] Solve 3 2 x - 7 = 5 . [5] Solve 3 2 x - 7 = 5 x +1 . [6] The number of bacteria in an experiment is modeled by the function N ( t ) = N 0 e - 2 t , where t is the time (in hours). a) Show that N (0) = N 0 . What does N 0 represent? (with respect to the experiment) b) Is the number of bacteria increasing or decreasing in time? c) If N 0 = 10000 , what is number of bacteria after 2 hours? [7] Solve 2 x 2 - x - 2 0 . [8] Consider f ( x ) = x x + 2 . a) What is the domain of f ? b) Calculate f - 1 . c) What is domain of f - 1 ? [9] Consider f : R R , f ( x ) = x + 1 if x 1 3 x - 1 if x > 1 a) Calculate f (0) , f (1) and f (2) . b) Solve f ( x ) = 2 . [10] a) What are the values of sin π 3 , sin 2 π 3 , arccos 1 and arccos 2 2 ? b) Given that x π , 3 π 2 and sin x = - 3 5 , calculate cos x and tan 2 x . (You’re allowed to use the Pocket-Trig-Sheet.) 1

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[11] Solve the inequality 2 | 2 - x |
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Exercises-Review_Part_I - MA100 Fall 2010 PART 1...

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