Test #4 33 QUESTIONS MATH1314 09281700 COLLEGE ALGEBRA Name atfm1314bli28 www.alvarezmathhelp.com website SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the equation b factoring. 1) 12 + 26 + 8 = 0 1) ALVAREZ VIDEO 4 M0-3,4,,8 M44-1,2 M2,9,11,12 Solve the equation using the quadratic formula. 2) 2 + 14 + 8 = 0 2) ALVAREZ VIDEO 8 M0-7 Solve the radical equation, and check all proposed solutions. 3) 30 + 1 = + 8 3) ALVAREZ VIDEO 9 m49-3 m0-9 math2 #16 math44 #4 1

Use the graph of the given function to find an relative maima and relative minima. 4) f() = 3-32 + 1 4 3 2 1 4) - -4-3 -2-1 1 2 3 4-1 -2-3 -4 - ALVAREZ VIDEO 1 M49- M2-21,22 Graph the function. ) f() = + 1 if < 1 4 if 1 ) - - ALVAREZ VIDEO 17 m49-6 m0- math2 #24 math44 # 2

f( + h) - f() Find and simplif the difference quotient, h 0 for the given function. h 6) f() = 2 + + 6 6) ALVAREZ VIDEO 18 m49-7 m0-11 math2 #2 math44 #6 Begin b graphing the standard absolute value function f() =. Then use transformations of this graph to graph the given function. 7) h() = - 3-3 7) 8 6 4 2 - -8-6 -4-2 -2 2 4 6 8-4 -6-8 - ALVAREZ VIDEO 21 m49-8 3

Find the domain of the function. 8) f() = 18-8) ALVAREZ VIDEO 23 m49-9 m0-12 math2 #30 math44 #7 Given functions f and g, perform the indicated operations. 9) f() = 2-6, g() = 9-8 Find f - g. 9) VIDEO ALVAREZ 2 M0-13 M49- M2-31 M44-8 ) f() = 3 + 2, g() = 2 + 8 Find fg. ) ALVAREZ VIDEO 28 M0-13 For the given functions f and g, find the indicated composition. 11) f() = 42 + 3 + 6, g() = 3-4 (g f)() 11) ALVAREZ VIDEO 31 m49-14 m0-14 math2 #3 math44 #9 4

Find the distance between the pair of points. 12) (-1, -3) and (-7, ) 12) ALVAREZ VIDEO 33 m49-1 m0-1 math2 #38 math44 # Graph the equation. 13) 2 + 2-8 - 4 + 11 = 0 13) - - - - ALVAREZ VIDEO 36 m49-17 m0-17 math2 #41 m,ath44 #12

Use the verte and intercepts to sketch the graph of the quadratic function. 14) f() = - 2-2 + 3 14) - - - - ALVAREZ VIDEO 38 M0-20 M49-19 M2-43 M44-13,14,1,16 Solve the problem. 1) An arrow is fired into the air with an initial velocit of 160 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given b the function h() = -16t 2 + 160t. Find the maimum height of the arrow. 1) ALVAREZ VIDEO 39 m49-20 math2 #44,4,46 6

Graph the polnomial function. 16) f() = 3 + 4 2 + - 6 16) - - - - ALVAREZ VIDEO 43 m49-22 m0-23 math2 #0 math44 #18 Solve the polnomial equation. In order to obtain the first root, use snthetic division to test the possible rational roots. 17) 3 + 82-18 + 20 = 0 17) ALVAREZ VIDEO 49 m49-24 m0-22 m2-0 m44-17 7

Find the vertical asmptotes, if an, of the graph of the rational function. - 49 18) 2-7 + 18) ALVAREZ VIDEO 4 m49-27 m0-26 math2 #6 math44 #21 Find the slant asmptote, if an, of the graph of the rational function. 19) f() = 2 + 6 - - 4 19) ALVAREZ VIDEO 7 m49-30 m0-2 math2 #8 math44 #20 Find the domain of the logarithmic function. 20) f() = ln (8 - ) 20) ALVAREZ VIDEO 63 m49-31 m0-30 math2 #61 math44 #24 8

Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 21) log 44 3-6( + ) 2 21) ALVAREZ VIDEO 67 m49-32 m0-31,32 m2-62,63,64 m44-2,26 #62,63,64 math44 2,26 Solve the equation b epressing each side as a power of the same base and then equating eponents. 22) 16 + 7 = 64-22) ALVAREZ VIDEO 70 m49-33 m0-33 math2 #6 math44 #27 Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 23) 3 + 6 = 8 23) ALVAREZ VIDEO 73 M0-34 M44-28 M49-36 9

Solve the logarithmic equation. Be sure to reject an value that is not in the domain of the original logarithmic epressions. Give the eact answer. 24) log 4 ( - 1) + log 4 ( - 7) = 2 24) ALVAREZ VIDEO 76 m49-37 m0-3 math2 #7 math44 #30 2) log 4 ( + 2) - log 4 = 2 2) ALVAREZ VIDEO 78 M0-37 26) log (4 + ) - log ( - 4) = log 3 26) ALVAREZ VIDEO 79 M0-37

27) ln + ln ( -1) = ln 72 27) ALVAREZLAB EXPONENZ (3,4) INTERACTMATH SEC 4.4 EXE 8 ALVAERZ VIDEO 80 m49-40,41 m0-36,37,38 math2 #81 math44 #32 Solve the problem. 28) Find out how long it takes a $30 investment to double if it is invested at 8% compounded semiannuall. Round to the nearest tenth of a ear. Use the formula 28) A = P 1 + r n nt. ALVAREZ VIDEO 81 M0-39 11

29) The function A = A0e -0.00866 models the amount in pounds of a particular radioactive material stored in a concrete vault, where is the number of ears since the material was put into the vault. If 900 pounds of the material are placed in the vault, how much time will need to pass for onl 19 pounds to remain? 29) ALVAREZ VIDEO 83 M0-40,42 M49-43 M44-34 30) The population of a certain countr is growing at a rate of 2.1% per ear. How long will it take for this countrʹs population to double? Use the formula t = ln 2, which gives the k time, t, for a population with growth rate k, to double. (Round to the nearest whole ear.) 30) ALVAREZ VIDEO 84 m49-44 m0-43 math2 #72 math44 #37 12

Solve the sstem of equations. 31) + + z = 2 - + 2z = -1 2 + + z = 1 31) ALVAREZ VIDEO 89 m49-46 m0-44 math2 #91 math44 #38 Find the indicated sum. 32) (i 2 + 6) 32) i = 3 ALVAREZ VIDEO 98 m49-47 m0-4 math2 #96 math44 #39 Write the first three terms in the binomial epansion, epressing the result in simplified form. 33) ( + 2) 16 33) ALVAREZ VIDEO 0 m49-49 m0-49 math2 #0,1 math44 #40 13

Answer Ke Testname: AAT4M1314BLIF2833W 1) - 4 3, - 2 2) {-7 + 3i, -7-3i} 3) {7} 4) maimum: (0, 1); minimum: (2, -3) ) (1, 4) (1, 2) - - 6) 2 + h + 7) 8 6 4 2 - -8-6 -4-2 -2 2 4 6 8-4 -6-8 - 8) (-, 18] 9) -7 + 2 ) 62 + 28 + 16 11) 122 + 9 + 14 12) 13) - - - - 14

Answer Ke Testname: AAT4M1314BLIF2833W 14) - - - - 1) 400 ft 16) - - - - 17) {1 + i, 1 - i, -} 18) = 2, = 19) = + 20) (-, 8) 21) log 4 + 4log + 1 log ( - ) - log 6-2log ( + ) 3 22) {44} 23) -4.11 24) {9} 2) { 2 1 } 26) {8} 27) {9} 28) 8.8 ears 29) 200 ears 30) 33 ears 31) {(-1, 2, 1)} 32) 68 33) 16 + 32 1 + 480 14 1