Precalculus11th EditionMichael Sullivan Publisher: PEARSONISBN: 9780135189405
Precalculus
Solutions for Precalculus
Problem 1RE:
In Problems 14, determine whether the function is a polynomial function, a rational function, or...Problem 2RE:
In Problems 14, determine whether the function is a polynomial function, a rational function, or...Problem 3RE:
In Problems 14, determine whether the function is a polynomial function, a rational function, or...Problem 4RE:
In Problems 14, determine whether the function is a polynomial function, a rational function, or...Problem 5RE:
In Problems , graph each function using transformation(shifting, compressing, stretching, and...Problem 6RE:
In Problems 57, graph each function using transformation(shifting, compressing, stretching, and...Problem 7RE:
In Problems 57, graph each function using transformation(shifting, compressing, stretching, and...Problem 8RE:
In Problems 811, graph each function by following Steps 1 through 5 on page 191. f(x)=x(x+2)(x+4)Problem 9RE:
In Problems 811, graph each function by following Steps 1 through 5 on page 191. f(x)=(x2)2(x+4)Problem 10RE:
In Problems 811, graph each function by following Steps 1 through 5 on page 191. f(x)=2x2+4x2Problem 12RE:
In Problems 1214, find the domain of each rational function. Find any horizontal, vertical, or...Problem 13RE:
In Problems 1214, find the domain of each rational function. Find any horizontal, vertical, or...Problem 14RE:
In Problems , find the domain of each rational function. Find any horizontal, vertical, or oblique...Problem 15RE:
In Problems 1520, graph each rational function following the seven steps on page 211. R(x)=2x6xProblem 19RE:
In Problems 1520, graph each rational function following the seven steps on page 211. R(x)=2x4(x1)2Problem 20RE:
In Problems 1520, graph each rational function following the seven steps on page 211. G(x)=x24x2x2Problem 26RE:
In Problems 26 and 27, find the remainder R when f(x) is divided by g(x). Is g a factor of f?...Problem 28RE:
Find the value of f(x)=12x68x4+1 at x=4.Problem 29RE:
In the Problems 29 and 30, use Descartess Rule of Signs to determine how many positive and negative...Problem 30RE:
In the Problems, use Descartes’s Rule of Signs to determine how many positive and negative real...Problem 32RE:
In the Problems , use the Rational Zeros Theorem to find all the real zeros of each polynomial...Problem 33RE:
In the Problems , use the Rational Zeros Theorem to find all the real zeros of each polynomial...Problem 34RE:
In the Problems , use the Rational Zeros Theorem to find all the real zeros of each polynomial...Problem 37RE:
In the Problems 37 and 38, find bounds on the real zeros of each number system. f(x)=x3x24x+2Problem 38RE:
In the Problems 37 and 38, find bounds on the real zeros of each number system. f(x)=2x37x210x+35Problem 39RE:
In the Problems and , use the Intermediate Value Theorem to show that each polynomial function has...Problem 40RE:
In the Problems 39 and 40, use the Intermediate Value Theorem to show that each polynomial function...Problem 41RE:
In the Problems 41 and 42, each polynomial function has exactly one positive zero. Approximate the...Problem 42RE:
In the Problems and , each polynomial function has exactly one positive zero. Approximate the zero...Problem 43RE:
In the Problems and , information is given about a complex polynomial whose coefficients are real...Problem 44RE:
In the Problems 43 and 44, information is given about a complex polynomial f whose coefficients are...Problem 45RE:
In the Problems , find the complex zeros of each polynomial function . Write in factored form.
45....Problem 46RE:
In the Problems 4548, find the complex zeros of each polynomial function f. Write f in factored...Problem 47RE:
In the Problems , find the complex zeros of each polynomial function . Write in factored form.
47....Problem 48RE:
In the Problems 4548, find the complex zeros of each polynomial function f. Write f in factored...Problem 50RE:
Making a Can A can in the shape of a right circular cylinder is required to have a volume of 250...Problem 51RE:
Housing Prices The data in the table on the right represents the January median new-home prices in...Problem 1CT:
Graph f(x)=(x3)42 using transformations.Problem 2CT:
For the polynomial function ,
Determine the maximum number of real zeros that the function may...Problem 3CT:
Find the complex zeros of f(x)=x34x2+25x100.Problem 4CT:
Solve in the complex number system.
Problem 5CT:
In problems 5 and 6, find the domain of each function. Find any horizontal, vertical, or oblique...Problem 6CT:
In problems and , find the domain of each function. Find any horizontal, vertical, or oblique...Problem 7CT:
Graph the function in Problem 6. Label all intercepts, vertical asymptotes, horizontal asymptotes,...Problem 8CT:
In Problems 8 and 9, write a function that meets the given condition. Fourth degree polynomial with...Problem 9CT:
Rational function; asymptotes: , ; domain :
Problem 10CT:
Use the Intermediate Value Theorem to show that the function has at least one zero on the interval...Problem 11CT:
Solve:
Problem 12CT:
Solve: x3+7x22x26x.Problem 1CR:
Find the distance between the points and .
Problem 2CR:
Solve the inequality x2x and graph the solution set.Problem 5CR:
Find the equation of the line parallel to the line and consisting the point. Express your answer...Problem 6CR:
Graph the equation.
Problem 7CR:
Does the relation {(3, 6), (1, 3), (2, 5), (3, 8)} represent a function? Why or why not?Problem 8CR:
Solve the equation x36x2+8x=0.Problem 15CR:
Given the function f(x)=x+5x1 What is the domain of f? Is the point (2,6) on the graph of f? If x=3,...Problem 16CR:
Graph the function f(x)=3x+7.Problem 17CR:
Graph f(x)=2x24x+1 by determining whether its graph is concave up or concave down and by finding its...Problem 18CR:
Find the average rate of change of from to . Use this result to find the equation of the secant...Problem 19CR:
In parts (a) to (f), use the following graph, Find the intercepts Based on the graph, tell whether...Problem 21CR:
For the function
Find the domain of .
Locate any intercepts.
Graph the function.
Based on the...Problem 22CR:
Graph the function f(x)=3(x+1)2+5 using transformations.Browse All Chapters of This Textbook
Chapter 1 - GraphsChapter 1.1 - The Distance And Midpoint FormulasChapter 1.2 - Graphs Of Equations In Two Variables; Intercepts; SymmetryChapter 1.3 - LinesChapter 1.4 - CirclesChapter 2 - Functions And Their GraphsChapter 2.1 - FunctionsChapter 2.2 - The Graph Of A FunctionChapter 2.3 - Properties Of FunctionsChapter 2.4 - Library Of Functions; Piecewise-defined Functions
Chapter 2.5 - Graphing Techniques: TransformationsChapter 2.6 - Mathematical Models: Building FunctionsChapter 3 - Linear And Quadratic FunctionsChapter 3.1 - Properties Of Linear Functions And Linear ModelsChapter 3.2 - Building Linear Models From DataChapter 3.3 - Quadratic Functions And Their PropertiesChapter 3.4 - Build Quadratic Models From Verbal Descriptions And From DataChapter 3.5 - Inequalities Involving Quadratic FunctionsChapter 4 - Polynomial And Rational FunctionsChapter 4.1 - Polynomial FunctionsChapter 4.2 - Graphing Polynomial Functions; ModelsChapter 4.3 - Properties Of Rational FunctionsChapter 4.4 - The Graph Of A Rational FunctionChapter 4.5 - Polynomial And Rational InequalitiesChapter 4.6 - The Real Zeros Of A Polynomial FunctionChapter 4.7 - Complex Zeros: Fundamental Theorem Of AlgebraChapter 5 - Exponential And Logarithmic FunctionsChapter 5.1 - Composite FunctionsChapter 5.2 - One-to-one Functions; Inverse FunctionsChapter 5.3 - Exponential FunctionsChapter 5.4 - Logarithmic FunctionsChapter 5.5 - Properties Of LogarithmsChapter 5.6 - Logarithmic And Exponential EquationsChapter 5.7 - Financial ModelsChapter 5.8 - Exponential Growth And Decay Models; Newton’s Law; Logistic Growth And Decay ModelsChapter 5.9 - Building Exponential, Logarithmic, And Logistic Models From DataChapter 6 - Trigonometric FunctionsChapter 6.1 - Angles, Arc Length, And Circular MotionChapter 6.2 - Trigonometric Functions: Unit Circle ApproachChapter 6.3 - Properties Of The Trigonometric FunctionsChapter 6.4 - Graphs Of The Sine And Cosine FunctionsChapter 6.5 - Graphs Of The Tangent, Cotangent, Cosecant, And Secant FunctionsChapter 6.6 - Phase Shift; Sinusoidal Curve FittingChapter 7 - Analytic TrigonometryChapter 7.1 - The Inverse Sine, Cosine, And Tangent FunctionsChapter 7.2 - The Inverse Trigonometric Functions (continued)Chapter 7.3 - Trigonometric EquationsChapter 7.4 - Trigonometric IdentitiesChapter 7.5 - Sum And Difference FormulasChapter 7.6 - Double-angle And Half-angle FormulasChapter 7.7 - Product-to-sum And Sum-to-product FormulasChapter 8 - Applications Of Trigonometric FunctionsChapter 8.1 - Right Triangle Trigonometry; ApplicationsChapter 8.2 - The Law Of SinesChapter 8.3 - The Law Of CosinesChapter 8.4 - Area Of A TriangleChapter 8.5 - Simple Harmonic Motion; Damped Motion; Combining WavesChapter 9 - Polar Coordinates; VectorsChapter 9.1 - Polar CoordinatesChapter 9.2 - Polar Equations And GraphsChapter 9.3 - The Complex Plane; De Moivre’s TheoremChapter 9.4 - VectorsChapter 9.5 - The Dot ProductChapter 9.6 - Vectors In SpaceChapter 9.7 - The Cross ProductChapter 10 - Analytic GeometryChapter 10.2 - The ParabolaChapter 10.3 - The EllipseChapter 10.4 - The HyperbolaChapter 10.5 - Rotation Of Axes; General Form Of A ConicChapter 10.6 - Polar Equations Of ConicsChapter 10.7 - Plane Curves And Parametric EquationsChapter 11 - Systems Of Equations And InequalitiesChapter 11.1 - Systems Of Linear Equations: Substitution And EliminationChapter 11.2 - Systems Of Linear Equations: MatricesChapter 11.3 - Systems Of Linear Equations: DeterminantsChapter 11.4 - Matrix AlgebraChapter 11.5 - Partial Fraction DecompositionChapter 11.6 - Systems Of Nonlinear EquationsChapter 11.7 - Systems Of InequalitiesChapter 11.8 - Linear ProgrammingChapter 12 - Sequences; Induction; The Binomial TheoremChapter 12.1 - SequencesChapter 12.2 - Arithmetic SequencesChapter 12.3 - Geometric Sequences; Geometric SeriesChapter 12.4 - Mathematical InductionChapter 12.5 - The Binomial TheoremChapter 13 - Counting And ProbabilityChapter 13.1 - CountingChapter 13.2 - Permutations And CombinationsChapter 13.3 - ProbabilityChapter 14 - A Preview Of Calculus: The Limit, Derivative, And Integral Of A FunctionChapter 14.1 - Investigating Limits Using Tables And GraphsChapter 14.2 - Algebra Techniques For Finding LimitsChapter 14.3 - One-sided Limits; ContinuityChapter 14.4 - The Tangent Problem; The DerivativeChapter 14.5 - The Area Problem; The IntegralChapter A.1 - Algebra EssentialsChapter A.2 - Geometry EssentialsChapter A.3 - PolynomialsChapter A.4 - Synthetic DivisionChapter A.5 - Rational ExpressionsChapter A.6 - Solving EquationsChapter A.7 - Complex Numbers; Quadratic Equations In The Complex Number SystemChapter A.8 - Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job ApplicationsChapter A.9 - Interval Notation; Solving InequalitiesChapter A.10 - Nth Roots; Rational ExponentsChapter B.1 - The Viewing RectangleChapter B.2 - Using A Graphing Utility To Graph EquationsChapter B.3 - Using A Graphing Utility To Locate Intercepts And Check For SymmetryChapter B.5 - Square Screens
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