Math 1A PDP Worksheet Rob Bayer August 27 2008 You should work on the following problems in groups of 3 Try to get through as many as you can but you aren t expected to finish everything Instead you should make sure everyone in your group knows how to solve all the problems and not just the answers A Review of PreCalc 1 Which of the following are functions 2 Sketch a graph of each of the following functions Be sure to correctly label any x or y intercepts as x 2 if x 1 well as any asymptotes a sin x b cos x c ex d ln x e x f f x x2 if x 1 3 Let f x be the function of a line that passes through the points 2 2 and 0 1 Find an algebraic description of f 4 Re write ln x 3 ln x 4 ln x2 1 in the form ln something 5 Simplify cos x tan x 2 e 2x ex 2x 1 ln e6 3x 2 x sec x 4 6 Solve the following inequalities a 1 x 3 4 b y 3 4 c x2 6x 8 0 Note you may want to write down your answer for future reference Even and Odd functions 1 Determine whether each of the following functions are e even o odd or n neither You should do this by both a graphing the function and b using the definitions of even and odd a f x x b g x x2 c p x ex d h t 3 t e f x sin x f q s s 3 2 For what positive integers n is f x xn even odd 3 a Show that no matter what function f you start with g x x h x f x f is odd 2 f x f x 2 is even and b Prove that every function f can be written as the sum of an even function and an odd function 4 Hard List all the functions that are both even and odd Domain and Range 1 Go back to the very first section of this worksheet and determine the domain and range of all the functions in problem 1 2 Find the domain of each of the following functions a b 3 x 1 1 ex x2 6x 8 3 d x2 6x 8 c e 1 ln x f 0 x if x 1 if x 1 g tan x x 1 h 4 2 1 x x 6x 8
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