MAT160FinalExamReview (6)
.pdf
School
Bergen Community College**We aren't endorsed by this school
Course
MAT 160
Subject
Mathematics
Date
Dec 19, 2024
Pages
10
Uploaded by DukePigeonMaster813
Cumulative Review for Intermediate AlgebraMATH-160Solve the given equation:1. 9x3= 12x42. (2y-1)(y+ 1) = (y-3)(y-2)3.7x-13=5x4.2x-1x2-2x-3-x-5x2+ 4x+ 3=xx2-95.y2+ 6y+ 11 = 2y2+ 9y-176.b6+ 7b3-8 = 07.√2x-1-√x+ 7 = 08.√3a+ 1 +a= 19.b1/2+ 3b1/4-10 = 010.3√2x-5 =-311. (x-7)2= 5612. 3x2-13x=-1913.|2a-5|=|a-3|14.|3(x-2) + 4|= 7Write the relation depicted in the diagram using ordered pair notation and deter-mine if it is a function:15.5278116.16491Find the domain of the given function:17.y=x2-5x+ 818.y=√2x-919.f(x) =3x√7-5x20.g(x) =x-72x2+ 9x-521.Givenf(x) = 2x-5, g(x) = 3x2-5x+ 2 andh(x) =x3-x, find :(a)g(5x+ 2)(b)f(x)-h(5)(c)f(x)[h(x)-g(x)]22.Givenf(x) = 2x2-5x+ 1, find (and simplify) :f(x+ 5)-f(x)523.Givenf(x) =x2-2x+ 5 andh(x) =x-23-2x, find (and simplify) :f[h(x)]Cerullo Learning Assistance CenterPage 1
Cumulative Review for Intermediate AlgebraMATH-16024.Givenf(x) =(x2+ 3ifx≤12x+ 1ifx >1(a)Find f(-4), f(1) and f(3)(b)Sketch the graphDetermine whether each function is one-to-one.Find the domain of the function,the inverse of the function and the domain of the inverse.If there is no inverse,state so.25.(a){(1,2), (-3,7), (5,8)}(b){(7,-3), (3,-8), (5,-3)}26.h(x) =x+ 1x-327.f(x) =x3-5Perform the indicated operation:28. (8x2-3xy+ 5y2)-[(4x2-1)-(2xy-7y2)]29. (x2+ 2x+ 3)(x-1)30. (4a-3b)331. 5x(x-1)-3x(x-1)2Factor completely:32. 125a3+ 8b333. 5ra+ 5rb-3sa-3sb34. 16x4-81y435. 9x2-9x-436.x4-8x2-9Divide:37. (8x3-1)÷(2x-1)38. (-46y2+ 18 + 33y-27y3+ 28y4)÷(4y-5)Perform the indicated operations. Express your answer in simplest form:39.3x2+ 4x-72x2-7x-152x2-5x-12x2+ 2x+ 1÷2x2-11x+ 12x2-140.3y2y-5-yy+ 3-6 + 12y2y2+y-15Cerullo Learning Assistance CenterPage 2
Cumulative Review for Intermediate AlgebraMATH-160Simplify the fraction and reduce in lowest terms:41.a-2525a2-45a42.4-49b26 +21bPerform the indicated operations. Express in the form a+bi:43.1 + 5i3-2i44. (2-5i)(3 +i)Perform the indicated operations and simplify: Assume all variables represent pos-itive real numbers. Write all answers with positive exponents.45. (a-9b-3c0)(a-5b2c-4)46.(5x-23+x-42)(x16)47.3x-2x-3x-1-348.2xy2x2y433x2y36349.x0y-6z3y4x-5z-250.(x12y13)-6(x14y15)-20xy13Perform the indicated operations. Express your answer in simplest radical form.51.3√33√7-√352.x2-3x-4√x+253.4x-10y√2x-√5y54. (√x+ 2)2-(√x+√2)2Solve the inequalities and graph the solutions on the number line:Express youranswer using interval notation.55. 2{x-[3-(5-x)]}>2-x56. 9<7-2(x-1)≤1757.|5a-4|+ 4>358.|2(x+ 1)-5x| ≥559.|b-6| ≤360. 2x2≤12-5x61. 6x2+ 7x+ 2>062. 10x2+ 9x+ 2≤0Write the equation of the line L satisfying the given condition:63.L passes through the points (-3, -1) and (-4, -6)64.L passes through (-2, -5) and is perpendicular to4x-3y= 1065.L passes through (1, -1) and is parallel to2y-3x= 12Cerullo Learning Assistance CenterPage 3
Cumulative Review for Intermediate AlgebraMATH-160Sketch the graph of the parabola, identify the vertex, intercepts, and axis of sym-metry:66.y=-(x-5)2+ 267.y= 3x2-6x+ 168.y=x2-5x69.y=-x2+ 4x-7Determine the type of function and sketch its graph:70.f(x) =√x-271.f(x) = 2x72.f(x) = 3-x73.f(x) =|x-5|+ 2Evaluate:74.(a) 6log68(b)log7(log77)(c)log2(-4)(d)log8164Solve the given equation for x:75.(a)log4x= 3(b)log913=x(c)logx27 = 3Use the properties of logarithms to express the given logarithms as a sum of simplerones:76.log5s25x4y3a277.log3x3√xyWrite the given expression as a single logarithm:78.12[log3a+log3b-(log319 + 4log3x)]79.log2x5+log2y7-log2z9Cerullo Learning Assistance CenterPage 4
Cumulative Review for Intermediate AlgebraMATH-160ANSWERS1.x= 0,x=342.y= 1,y=-73.x= 64.x=325.y=-7,y= 46.b= 1,b=-27.x= 88.a= 09.b= 1610.x=-1111. 7±2√1412.13±√59i613.a= 2,a=8314.x= 3,x=-5315.{(5,2),(5,7),(8,1)};It is not a function16.{(4,1),(9,1),(1,6)};It is a function17.All real numbers or(-∞,∞)18.x|x≥9219.x|x <7520.x|x6=-5, x6=1221.(a) 75x2+ 35x+ 4(b) 2x-125(c) 2x4-11x3+ 23x2-24x+ 1022. 4x+ 523.25x2-78x+ 61(3-2x)224. (a)f(-4) = 19,f(1) = 4, f(3) = 7(b)xy-20242468(-2,7)(1,4)(0,3)(-1,4)(1,3)(2,5)(3,7)25.(a)Domain:{-3,1,5}Inverse:{(2,1),(7,-3),(8,5)}Domain of Inverse:{2,7,8}(b)Domain:{3,5,7}Since the set is not a one-to-onefunction, there isNo Inverse26.(a)Domain:{x|x6= 3}or (-∞,3)∪(3,∞)Inverse:h-1(x) =3x+1x-1Domain of Inverse:{x|x6= 1}or(-∞,1)∪(1,∞)27.(a)Domain:Allrealnumbersor(-∞,∞)Inverse:f-1(x) =3√x+ 5Domain off-1(x) :All real num-bers or(-∞,∞)28. 4x2-xy-2y2+ 129.x3+x2+x-330. 64a3-144a2b+ 108ab2-27b331.-3x3+ 11x2-8xCerullo Learning Assistance CenterPage 5
Cumulative Review for Intermediate AlgebraMATH-16032. (5a+ 2b)(25a2-10ab+ 4b2)33. (5r-3s)(a+b)34. (2x-3y)(2x+ 3y)(4x2+ 9y2)35. (3x-4)(3x+ 1)36. (x2+ 1)(x+ 3)(x-3)37. 4x2+ 2x+ 138. 7y3+ 2y2-9y-3 +34y-539.(3x+ 7)(x-1)2(x-5)(x+ 1)(2x-3)40.y2+ 2y-6(2y-5)(y+ 3)41.a5a+ 242.(2b-7)3b43.-713+1713i44. 11-13i45.1a14bc446.5x1/2+1x11/6or5√x3+6√xx247.x122748.x3y349.x5z5y1050.1x9y19/351.3(√21 + 1)2052. (x+ 1)(√x-2)53. 2(√2x+q5y)54.-2√2x55. (-2,∞)-5-4-3-2-1012356. [-4,0)-4-3-2-10123457. (-∞,∞)58. (-∞,-1]∪73,∞-4-3-2-1012347359. [3,9]234567891060.-4,32-6-5-4-3-2-101233261.- ∞,-23-12,∞-10-23-1262.-12,-25-10-25-1263.y= 5x+ 1464.y=-34x-13265.y=32x-52Cerullo Learning Assistance CenterPage 6
Cumulative Review for Intermediate AlgebraMATH-16066.x-intercepts:(5 +√2,0),(5-√2,0)y-intercepts:(0,-23)vertex:(5,2)axis of symmetry:x= 5y=-(x-5)2+ 2xy2468-8-6-4-2246(3,-2)(4,1)(5,2)(6,1)(7,-2)67.x-intercepts:3±√63,0!y-intercepts:(0,1)vertex:(1,-2)axis of symmetry:x= 1y= 3(x)2-6x+ 1xy-2246-2246810(0,1)(1,-2)(2,1)(-1,10)(3,10)Cerullo Learning Assistance CenterPage 7
Cumulative Review for Intermediate AlgebraMATH-16068.x-intercepts:(0,0),(5,0)passes thru the origin:(0,0)vertex:(52,-254)axis of symmetry:x=52y= (x)2-5xxy-1123456-7-6-5-4-3-2-11252,-254(1,-4)(4,-4)69.x-intercepts: None;y-intercepts:(0,-7)vertex:(2,-3)axis of symmetry:x= 2y=-(x)2+ 4x-7xy-2246-8-6-4-2(2,-3)(1,-4)(3,-4)Cerullo Learning Assistance CenterPage 8
Cumulative Review for Intermediate AlgebraMATH-16070.Square Root Functionf(x) =√x-212345624xy71.Exponential Functiony= 2x-11234246xy72.Exponential Functionf(x) = 3-x1234246xy73.Absolute Value Functionf(x) =|x-5|+ 2xy-112345678-11234567(5,2)(4,3)(6,3)(3,4)(7,4)Cerullo Learning Assistance CenterPage 9
Cumulative Review for Intermediate AlgebraMATH-16074.(a) 8(b) 0(c)DNE(d) -275.(a)x= 64(b)x=-12(c)x= 376.12(2 + 4log5x+ 3log5y-2log5a)77. 3log3x-12log3x-12log3y78.log3sab19x479.log29xy35zCerullo Learning Assistance CenterPage 10