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This 4 page Class Notes was uploaded by Green Lesch on Monday September 28, 2015. The Class Notes belongs to MATH1041 at Temple University taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/215467/math1041-temple-university in Mathematics (M) at Temple University.
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Date Created: 09/28/15
0 00 a 01 a 1 The graph of a function f is given The graphs of f and g are given MATH 1041 BEGINNING OF SEMESTER REVIEW PROBLEMS FALL 2007 a State the value of f71 b Estimate the value of f2 c For what values of z is f 2 1 Estimate the values of x such that f 0 e State the domain and range of f f On what interval is f increasing a State the values of f74 and 93 b For what values of z is f 9x c Estimate the solution of the equation f 71 d On what interval is f decreasing e State the domain and range of f f State the domain and range of g g Estimate Show your steps 1 f 0 9X3 ii 9 0 f4 iii f O f0 Express the side length of a square as a function of the length d of the squares diagonal Then express the area as a function of the diagonal length A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 in by 22 in by cutting out equal squares of side x at each corner and then folding up the sides as in the gure Express the volume V of the box as a function of x l 22 J x x39 I 11 L 11 I I quotI x x 31quot Find the domain of the function 1 a fx1 W 390 f 96 Graph the functions For each function determine its domain and range a fz572z b f 172z7x2 z if0 x 1 27 if 1lt 2 37 2x ifz 1 ifzgt1 C f96 d 1 1 Graph the functions by shifting the graphs of the functions V or 7 as appropriate For each function determine its domain and range ltagtyW4 ltbgty 2 cm 8 Find the domains of f7 9 f g and f g a f96967 996W1 b f96wc17 996W 1 9 Find the domains of f7 9 fg7 and gf if f95 2 995 9521 10 If f z 5 and g x2 7 37 nd the following a 1790 390 900 C f996 d 90 11 If 4x 7 57 Ms 2 and fx 1x7 nd formulas for the following a u f95 b HUWW C fu 95 12 21 Write a formula for f o g and g o f and b nd the domain of each we 7 m gm 7 13 Complete the following table 9C f0 f O a x77 7 b z2 3x 7 c 7 75 275 s d 7 71 71 1 e 7 17 z 1 f 7 7 z s 14 Complete the following table of function values If the function is unde ned at a given angle7 enter UND Do not use a calculator or tables 7T 37139 7r 6 77139 0 7 7 77 6 7T 2 4 3 sin 6 cos 6 tan 6 cot 6 sec 6 cs0 6 15 Graph the functions What is the period of each function a sin 2x b sinx2 c cos 7 1 cos x 7 3 16 Find cosx and tans if sing7 ifxE 3 17 Determine which of the following graphs are graphs of functions of z and which are not Give reasons for your answers a b c d y y y 0 0 0 39 0 18 Say whether the function is even7 odd7 or neither Give reasons for your answer a we 3 b we x2 1 c we z x d we x3 x 19 Which of the functions whose graphs are shown below are even7 which are odd7 and which are neither even nor odd Which of the functions are oneto one and which are not 20 Each of exercises7 a and b7 gives a formula for a function y f and shows the graphs of f and f l Find a formula for f 1 in each case Identify the domain and range of f l a f21 20 b fzz371 v J39m 21 Solve for x a 9513 2 b 953 712 c 71 5 d 39527295 6z e z274z7 0 2xz727x273 7 2 2 7 1 QW O glm T 22 Solve the following inequalities ltx3gtltx71gt gt 23L17x 37 b 7228 0 c 2 0 7 23 In each exercise7 sketch the given curves together in the same coordinate plane and label each curve with its equation a 1123 113 112m b yem and 116m 24 Use the laws of exponents to simplify the expressions a 913 916 b 25184 c MW 25 Express the following logarithrns in terms of ln 2 and ln 3 a ln075 b ln49 c ln12 d ln3 e ln3 f nix135 26 Use the properties of logarithrns to simplify the expressions a Mme 7 ln b ln32 7 9x 111 c In4t4 71n2 27 Find sirnpler expressions for the quantities a 611172 671nm2 c elnmilny d 21nE e lnln 68 lne w2 y2 28 Solve for y in terms oft or x as appropriate 21 lny 2t4 b lny71 iln2 xlnx c lny271 ilny1 lnsin s 29 Solve for t a 57W 7 27 b a 7 c 5011Mt 7 04 d M 7952
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