Review Final ExamName___________________________________ Date: _________________________Use the graph to determine the function's domain andrange.1)Use the graph of f to draw the graph of its inversefunction.2)Find functions f and g so that h(x) =(f g)(x).3) h(x) =10x2+8Factor the trinomial, or state that the trinomial is prime.4) 15x2+8x - 165) x2+11x +24Find the domain of the function.6) g(x) =2xx2 - 1Graph the given functions on the same rectangularcoordinate system. Describe how the graph of g is relatedto the graph of f.7) f(x) = x3, g(x) = x3+4Find the product and write the result in standard form.8) (1 + 4i)(1 - 4i)Does the graph represent a function that has an inversefunction?9)Find the inverse of the one-to-one function.10) f(x) = x +6Factor completely, or state that the polynomial is prime.11) 2x3 - 18x1Identify the intervals where the function is changing asrequested.12) DecreasingGiven functions f and g, perform the indicated operations.13) f(x) = 4x - 4, g(x) = 6x - 5Find f -g.Graph the line whose equation is given.14) y =35x +3Find the domain of the composite function fg.15) f(x) = x;g(x) = 5x + 5Factor completely, or state that the polynomial is prime.16) x3 - 6x2 - 25x + 150For the given functions f and g , find the indicatedcomposition.17) f(x) =4x +4, g(x) =76x(fg)(x)Determine whether the given function is even, odd, orneither.18) f(x) = x5 -x4Find the inverse of the one-to-one function.19) f(x) =57x +6Perform the indicated operations and write the result instandard form.20) ( 10 - - 36)( 10 + - 36)Factor completely, or state that the polynomial is prime.21) 7x3 - 7Add or subtract as indicated and write the result instandard form.22) -3-(- 3- 10i) -(-2 +2i)Factor the perfect square trinomial.23) 64x2- 16x + 1Graph the function.24) f(x) =x +1 if-7 x < 5-7 if x = 5- x +8 if x > 5Find an nth degree polynomial function with realcoefficients satisfying the given conditions.25) n = 3; 2 and 3 + 2i are zeros; leading coefficientis 1Use Descartes's Rule of Signs to determine the possiblenumber of positive and negative real zeros for the givenfunction.26) f(x) = 3x8- 4x7 + x6 - 1.5x + 82Graph f as a solid line andf-1 as a dashed line in thesame rectangular coordinate space. Use interval notationto give the domain and range of f and f-1.27) f(x) = (x - 1)2, x 1Solve the polynomial inequality and graph the solutionset on a number line.Express the solution set in intervalnotation.28) 16x3 + 48x2 - 25x - 75 > 029) 15x2 < 14x + 1Solve the rational inequality and graph the solution set ona real number line. Express the solution set in intervalnotation.30)3xx + 6< xFind a rational zero of the polynomial function and use itto find all the zeros of the function.31) f(x) = x3- 5x2+17x - 1332) f(x) = x4 + 4x3 -11x2 -26x -12Divide using long division.33) (24x3 + x2- 48x - 2) (8x2 - 16)Divide using synthetic division.34)x5 + x3- 1x - 2Find the range of the quadratic function.35) f(x) = - x2+8x - 6Determine whether the given quadratic function has aminimum value or maximum value. Then find thecoordinates of the minimum or maximum point.36) f(x) = -2x2- 6xSolve the problem.37) You have 104 feet of fencing to enclose arectangular plot that borders on a river. If youdo not fence the side along the river, find thelength and width of the plot that willmaximize the area.For the following problem,answer items a-f.a) Determine if f(x) has any symmetryb) Find the y-interceptc) Find the x-intercepts, if anyd) Find the equation of the vertical asymptote(s) and/orhole(s), if anye) Find the equation of the horizontal/slant asymptote, ifanyf) Graph the function. (Find any additional points, ifneeded)38) f(x) =x2+3x - 10x2- 4339) f(x) =2xx2- 4For the following problem, answer questions a-d.a) Determine the end behaviorb) Find the x-intercepts, their multiplicities and state if ittouches or crosses the x-axis at each interceptc) Find the y-interceptd) Graph the function. (Plot any additional points, ifneeded)40) f(x) = x4- 3x3 - x2+341) f(x) = x4 -4x242) f(x) = x4 -4x3 + 4x2Use the vertex and intercepts to sketch the graph of thequadratic function.43) f(x) = - 4(x - 4)2- 544) f(x) = - x2 + 4x + 5Solve the equation by expressing each side as a power ofthe same base and then equating exponents.45) 9x + 2 = 27x - 84Solve the logarithmic equation. Be sure to reject any valuethat is not in the domain of the original logarithmicexpressions. Give the exact answer.46) log6 (x2- 5x) = 1Use properties of logarithms to expand the logarithmicexpression as much as possible. Where possible, evaluatelogarithmic expressions without using a calculator.47)log24x2y4Use properties of logarithms to condense the logarithmicexpression.Write the expression as a single logarithmwhose coefficient is 1.Where possible, evaluatelogarithmic expressions.48) 5 log74 +15log7 (r - 1) -12log7 rGraph the function.49) Use the graph of f(x) = log x to obtain thegraph of g(x) = 3 -log x.Solve the exponential equation. Express the solution set interms of natural logarithms.50) 4x + 4 = 52x + 5Solve the system by the substitution method.51) x -2y = 3x2 -xy = 20Solve the system by the addition method.52) 9x2 + y2 = 819x2 - y2 = 81Graph the function.53) Use the graph of f(x) = 5x to obtain the graphof g(x) = 5x +2- 2.Solve the problem.54) Find out how long it takes a $2500 investmentto double if it is invested at 9% compoundedmonthly. Round to the nearest tenth of a year.Use the formula A = P 1 +rnnt.Solve.55) A fossilized leaf contains 27% of its normalamount of carbon 14. How old is the fossil (tothe nearest year)? Use 5600 years as thehalf- life of carbon 14.Solve the problem.56) The logistic growth function f(t) =4801 + 5.9e-0.29t describes the population of aspecies of butterflies t months after they areintroduced to a non- threatening habitat. Howmany butterflies are expected in the habitatafter 19 months?Solve the logarithmic equation. Be sure to reject any valuethat is not in the domain of the original logarithmicexpressions. Give the exact answer.57) ln (x - 8) -ln (x + 8) = ln (x - 4) -ln (x + 10)Solve the system by the substitution method.58) x + y = 32y = x2- 4x +45Solve the system by the addition method.59) 4x2- 3y2 = 245x2+5y2 = 65Solve the system of equations.60)x + y = 12x +2y - 5z = - 3x - z = 2Solve the system by the method of your choice. Identifysystems with no solution and systems with infinitelymany solutions, using set notation to express theirsolution sets.61) y = 10 - 2x8x + 4y = 40Graph the solution set of the system of inequalities orindicate that the system has no solution.62) 4x -y 8x +2y 263) y > x24x + 6y 2464) x2 + y2 368x +2y 1665) x2 + y2 64y - x2 > 0Solve the problem.66)Let A =-7 4 6- 5 4 - 45 1 4 and B =6 2 - 79 2 -1-74 - 5. Find-2A +3B.Find the product AB, if possible.67) A =- 1 35 2,B =0 - 2 51 - 3 268)A =3 - 2 10 4 -2,B =5 0- 2 36Solve the system of equations using matrices. UseGauss-Jordan elimination.69)7x- y +3z = 752x +9y - 3z = 13- 4x - 7y + z = - 39Use Cramer's rule to solve the system.70)3x - 7y +6z = 16- 7x +4y +2z = - 46-5x - 9y - 2z = -60Solve the system using the inverse that is given for thecoefficient matrix.71)x + 2y + 3z = 5x + y + z = - 52x + 2y + z = 7 The inverse of 1 2 31 1 12 2 1 is - 1 4 - 11- 5 20 2 - 1.Find the inverse of the matrix, if possible.72)A =- 5 01 -473)A =1 0 04 1 00 -9 1Use Cramer's rule to solve the system.74) 7x + 8y = 42x + 3y = 2Use Gaussian elimination to find the complete solution tothe system of equations, or state that none exists.75) 4x -y + 3z = 12x + 4y + 6z = - 325x + 3y + 9z = 207Answer KeyTestname: FINAL EXAM REVIEW1) domain: [0, )range: [-3, )2)3) f(x) = x +8, g(x) = 10/x24) (3x +4)(5x - 4)5) (x +3)(x +8)6) (- , - 1)(- 1, 1)(1, )7) g shifts the graph of f vertically up 4 units8) 179) No10) f- 1(x) = x2- 611) 2x(x + 3)(x - 3)12) (- 3, - 2)13) -2x +18Answer KeyTestname: FINAL EXAM REVIEW14)15) [-1, )16) (x - 6)(x + 5)(x - 5)17)24x7 +24x18) Neither19) f- 1(x) =57x- 6720) 4621) 7(x -1)(x2 + x + 1)22) 2+8i23) (8x - 1)224)25) f(x) = x3- 8x2+25x - 2626) 4, 2 or 0 positive zeros, no negative zeros9Answer KeyTestname: FINAL EXAM REVIEW27)f domain = (1, ); range = (0, )f- 1 domain = (0, ); range = (1, )28) -3, - 54 54, 29) - 115, 130) (- 6, - 3)(0, )31) {1, 2+ 3i, 2- 3i}32) {- 1, 3, - 3 + 5, - 3 - 5}33) 3x +1834) x4+2x3+5x2+10x +20+39x - 235) (- , 10]36) maximum;-32, 9237) length: 52 feet, width: 26 feet10Answer KeyTestname: FINAL EXAM REVIEW38)39)40)11Answer KeyTestname: FINAL EXAM REVIEW41)42)43)12Answer KeyTestname: FINAL EXAM REVIEW44)45) {28}46) {6, - 1}47)12log2 x +14log2 y -1248) log710245r - 1r49)50)5 ln 5 -4 ln 4ln 4 -2 ln 551) {(5, 1), (- 8, -112)}52) {(3, 0), (- 3, 0)}13Answer KeyTestname: FINAL EXAM REVIEW53)54) 7.7 years55) 10,55956) 469 butterflies57) - 2458) {(7, 25), (- 4, 36)}59) {(3, 2), (-3, 2), (3, -2), (-3, -2)}60) {(3, -2, 1)}61) {(x, y)2x + y = 10}62)63)14Answer KeyTestname: FINAL EXAM REVIEW64)65)66)32 -2 - 3337 -2 5- 31 10 - 2367)3 - 7 12 -162968) AB is not defined.69) {(8, 2, 7)}70) {(8, 2, 1)}71) {(- 32, 44, - 17)}72)-150- 120- 1473)1 0 0- 4 1 0- 36 9 174) {(- 45, 65)}75) 15