Precalculus11th EditionMichael Sullivan Publisher: PEARSONISBN: 9780135189405
Precalculus
Solutions for Precalculus
Problem 1AYU:
Suppose that the graph of a function f is known. Then the graph of y=f( x2 ) may be obtained by a(n)...Problem 2AYU:
Suppose that the graph of a function f is known. Then the graph of y=f( x ) may be obtained by a...Problem 3AYU:
True or False The graph of y= 1 3 g( x ) is the graph of y=g( x ) stretched by a factor of 3.Problem 4AYU:
True or False The graph of y=f( x ) is the reflection about the x-axis of the graph of y=f( x ) .Problem 5AYU:
Which of the following functions has a graph that is the graph of y= x shifted down 3 units? a. y=...Problem 6AYU:
Which of the following functions has a graph that is the graph of y=f( x ) compressed horizontally...Problem 7AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 8AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 9AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 10AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 11AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 12AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 13AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 14AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 15AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 16AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 17AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 18AYU:
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C....Problem 19AYU:
In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Shifted to the...Problem 20AYU:
In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Shifted to the...Problem 21AYU:
In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Shifted up 4...Problem 22AYU:
In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Shifted down 4...Problem 23AYU:
In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Reflected about...Problem 24AYU:
In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Reflected about...Problem 25AYU:
In Problems, write the function whose graph is the graph of but is:
Vertically stretched by a...Problem 26AYU:
In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Horizontally...Problem 27AYU:
In Problems, write the function whose graph is the graph of but is:
Horizontally compressed by a...Problem 28AYU:
In Problems 1928, write the function whose graph is the graph of y=x3, but is: Vertically compressed...Problem 29AYU:
In Problem 27-30, find the function that is finally graphed after each of the following...Problem 30AYU:
In Problem 27-30, find the function that is finally graphed after each of the following...Problem 31AYU:
In Problems 2932, find the function that is finally graphed after each of the following...Problem 32AYU:
In Problem 27-30, find the function that is finally graphed after each of the following...Problem 33AYU:
In Problem 27-30, find the function that is finally graphed after each of the following...Problem 34AYU:
In Problem 27-30, find the function that is finally graphed after each of the following...Problem 35AYU:
In Problem 27-30, find the function that is finally graphed after each of the following...Problem 36AYU:
In Problem 27-30, find the function that is finally graphed after each of the following...Problem 37AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 38AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 39AYU:
In Problems graph each function using the techniques of shifting, compressing, stretching, and/or...Problem 40AYU:
In Problems 3760, graph each function using the techniques of shifting, compressing, stretching,...Problem 41AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 42AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 43AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 44AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 45AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 46AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 47AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 48AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 49AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 50AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 51AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 52AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 53AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 54AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 55AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 56AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 57AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 58AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 59AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 60AYU:
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching,...Problem 61AYU:
In Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step...Problem 62AYU:
In Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step...Problem 63AYU:
In Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step...Problem 64AYU:
In Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step...Problem 65AYU:
In Problems 69-76, complete the square of each quadratic expression. Then graph each function using...Problem 66AYU:
In Problems 69-76, complete the square of each quadratic expression. Then graph each function using...Problem 67AYU:
In Problems 69-76, complete the square of each quadratic expression. Then graph each function using...Problem 68AYU:
In Problems 69-76, complete the square of each quadratic expression. Then graph each function using...Problem 69AYU:
In Problems 69-76, complete the square of each quadratic expression. Then graph each function using...Problem 70AYU:
In Problems 69-76, complete the square of each quadratic expression. Then graph each function using...Problem 71AYU:
In Problems 69-76, complete the square of each quadratic expression. Then graph each function using...Problem 72AYU:
In Problems 69-76, complete the square of each quadratic expression. Then graph each function using...Problem 73AYU:
Suppose that the -intercepts of the graph of are and.
What are the -intercepts of the graph of...Problem 74AYU:
Suppose that the -intercepts of the graph of are and.
What are the -intercepts of the graph of...Problem 75AYU:
Suppose that the function is increasing on the interval.
Over what interval is the graph of ...Problem 76AYU:
Suppose that the function y=f(x) is decreasing on the interval [2,7]. Over what interval is the...Problem 77AYU:
77. The graph of a function f is illustrated in the figure. (a) Draw the graph of y=| f( x ) | . (b)...Problem 78AYU:
78. The graph of a function f is illustrated in the figure. (a) Draw the graph of y=| f( x ) | . (b)...Problem 79AYU:
79. Suppose ( 1,3 ) is a point on the graph of y=f( x ) . (a) What point is on the graph of y=f( x+3...Problem 80AYU:
80. Suppose ( 3,5 ) is a point on the graph of y=g( x ) . (a) What point is on the graph of y=g( x+1...Problem 81AYU:
81. Graph the following functions using transformations. (a) f( x )=int( x ) (b) g( x )=int( x )Problem 82AYU:
82. Graph the following functions using transformations. (a) f( x )=int( x1 ) (b) g( x )=int( 1x )Problem 83AYU:
83. (a) Graph f( x )=| x3 |3 using transformations. (b) Find the area of the region that is bounded...Problem 84AYU:
84. (a) Graph f( x )=2| x4 |+4 using transformations. (b) Find the area of the region that is...Problem 85AYU:
85. Thermostat Control Energy conservation experts estimate that homeowners can save 5% to 10% on...Problem 86AYU:
Digital Music Revenues The total worldwide digital music revenues R, in billions of dollars, for the...Problem 87AYU:
87. Temperature Measurements The relationship between the Celsius ( C ) and Fahrenheit ( F )s...Problem 88AYU:
88. Period of a Pendulum The period T (in seconds) of a simple pendulum is a function of its length...Problem 89AYU:
89. The equation y= ( xc ) 2 defines a family of parabolas, one parabola for each value of c . On...Problem 91AYU:
Challenge Problem If a function is increasing on the intervals and and decreasing on the...Problem 92AYU:
Challenge Problem In statistics, the standard normal density function is given by. This function can...Problem 93AYU:
91. Suppose that the graph of a function f is known. Explain how the graph of y=4f( x ) differs from...Problem 94AYU:
92. Suppose that the graph of a function f is known. Explain how the graph of y=f( x )2 differs from...Problem 95AYU:
93. The area under the curve y= x bounded front below by the x-axis and on the right by x=4 is 16 3...Problem 96AYU:
94. Explain how the range of the function f( x )= x 2 compares to the range of g( x )=f( x )+k .Problem 97AYU:
95. Explain how the domain of g( x )= x compares to the domain of g( xk ) , where k0 .Problem 98AYU:
Problems 96-99 are based on material learned earlier in the course. The purpose of these problems is...Problem 99AYU:
Angie runs mph for the first half of the marathon, miles, but twists her knee and must walk mph...Problem 100AYU:
Find the amount of water used in a -minute shower if the gallons of water used when taking a...Problem 101AYU:
Problems 96-99 are based on material learned earlier in the course. The purpose of these problems is...Problem 102AYU:
Find the domain of h(x)=x+2x25x14.Problem 103AYU:
Projectile MotionA ball is thrown upward from the top of a building, Itsheight h, in feet, after t...Problem 104AYU:
Simplify.
Problem 105AYU:
Find the difference quotient of.
Problem 106AYU:
Factor z3+216.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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