Rob Bayer Math 1A PDP Worksheet August 27, 2008You should work on the following problems in groups of 3. Try to get through as many as you can, but youaren’t expected to finish everything. Instead, you should make sure everyone in your group knows how tosolve all the problems, and not just the answers.A Review of PreCalc1. 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 aswell as any asymptotes: a) sin x, b) cos x, c) ex, d) ln x, e) |x|, f) f(x) =(x + 2 if x > 1x2if x ≤ 13. Let f (x) be the function of a line that passes through the points (−2, 2) and (0, 1). Find an algebraicdescription 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−2xex+1sec2x+2x4x−3√xln e66. Solve the following inequalities:(a)1x−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 functions1. Determine whether each of the following functions are (e) even, (o) odd, or (n) neither. You shoulddo 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 + 32. For what positive integers n is f(x) = xneven? odd?3. (a) Show that no matter what function f you start with, g(x) =f(x)+f(−x)2is even andh(x) =f(x)−f(−x)2is odd.(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 Range1. Go back to the very first section of this worksheet and determine the domain and range of all thefunctions in problem (1).2. Find the domain of each of the following functions:(a)3x−1(b)1ex(c)√x2− 6x + 8(d)3√x2− 6x + 8(e)1ln x(f)(√x if x ≥ 10 if x < 1(g) tan x(h)√x1 − x+14√x2− 6x +
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