Math 131 Exam 1 Review 1 Find the domain of each function f x a 100 x 2 g x 2 3x 2 b 1 100 x 2 c x2 9 d ln x 2 e ln x 2 2 A tax schedule requires you to pay 15 of the first 20000 of income plus 20 of the amount above 20000 For example a person earning 50000 pays 15 of 20000 plus 20 of 30000 Write the tax as a piecewise function of income x 3 f x is a transformation of y x 2 The range of f is 12 f 3 12 and f 0 6 You do not need a horizontal distortion Write the formula for f x 4 f x is a transformation of y ln x f x approaches minus infinity as x approaches 2 f 3 7 and f e 2 10 Write a formula for f x assuming no x distortion was done 5 Solve for A B and C if f x A Be Cx f x 3 as x f 0 8 f 1 7 List the transformations of y e in a proper order that result in f x x 6 A culture begins with 100 cells and grows exponentially so that after 2 hours there are 250 cells Find N t the number of cells after t hours 7 Give two possibilities for f and g if f g x x 2 2 x 1 1 3 8 An account earning continuous compound interest had the values shown at ends of the first through the fifth years year x 1 2 3 4 5 account value 1056 54 1116 28 1179 40 1246 08 1316 58 a Do an exponential regression and write the exponential model Write the model in base e using b e ln b Estimate the annual interest rate and the initial principal b According to the model what is the approximate doubling time tripling time c If the y values in the table were replaced by lny which model would best fit d If the x and y values in the table were switched which model would best fit f ex 2 3 x 9 Solve for x if a e 2 x 2 e x 1 16 b e 2 x 3e x 2 0 10 Solve for x exactly a e 3 ln 2 x d log 4 x 2 9 2 log 4 x 12 5 log 4 5 2 3 b e log 4 x 3 log 4 x 3 2 c log 3 3 x 2 log 3 x 2 3 Section 2 1 problem 11 A particle travels in a straight line The directed distance from a reference point is given by d t ft where t is in seconds Find the average velocity for t between 1 and 3 secs Find the instantaneous velocity at t 1 sec a d t 8t 12 b d t 60 t 16 t 2 c d t 15 t 12 Evaluate each limit or state DNE if it does not exist x 2 x 20 a lim d lim x ln x 2 x 4 b x 2 16 x 0 e lim x 4 x 2 x 20 x 2 16 lim e1 x f x 0 c lim e1 x x 0 lim x 5 g x 2 x 20 x 2 16 lim x 2 13 Find the value of c which makes f x continuous for all x x 2 cx 1 x 2 f x 7x 2 x 14 sin x x 0 x f x 1 x 0 x ln x 0 x Find a lim f x and x 0 b lim f x x 0 Is f left continuous at 0 right continuous at 0 both or neither sin 2 x 1 sin x 1 15 Find all discontinuities of f x and give either a graphical or a definition reason for each discontinuity x 2 5x 6 2 x 2x f x 2 x 3 5 x 11 x 1 x 1 1 x 5 5 x Section 2 5 problem 16 Find each limit as a number infinity or minus infinity or state DNE x 1 1 a lim e x d lim x x f lim x b lim e x 2 x x 4 2x3 e x 2 10 x2 7x c lim x x 2 3x lim x x 5 4 x 4 27 x 2 2x 5 x 3 15 x 2 3 7 x 3 25 17 Find the inverse function for each a f x 4e x 2 b f x ln 7 x 3
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