Math1010text.idx

\indexentry{set ! definition of|hyperpage}{1}
\indexentry{set ! verbal description|hyperpage}{1}
\indexentry{set ! roster method|hyperpage}{1}
\indexentry{set ! set-builder notation|hyperpage}{1}
\indexentry{set-builder notation|hyperpage}{1}
\indexentry{set ! inclusion|hyperpage}{2}
\indexentry{$\in $|hyperpage}{2}
\indexentry{set ! exclusion|hyperpage}{2}
\indexentry{$\notin  $|hyperpage}{2}
\indexentry{subset ! definition of|hyperpage}{2}
\indexentry{set ! intersection|hyperpage}{2}
\indexentry{intersection of two sets|hyperpage}{2}
\indexentry{set ! union|hyperpage}{2}
\indexentry{union of two sets|hyperpage}{2}
\indexentry{set ! empty|hyperpage}{3}
\indexentry{empty set|hyperpage}{3}
\indexentry{diagram ! Venn Diagram|hyperpage}{3}
\indexentry{Venn Diagram|hyperpage}{3}
\indexentry{real number ! set of|hyperpage}{3}
\indexentry{real number ! definition of|hyperpage}{3}
\indexentry{set ! sets of numbers|hyperpage}{4}
\indexentry{set ! empty|hyperpage}{4}
\indexentry{empty set|hyperpage}{4}
\indexentry{natural number ! set of|hyperpage}{4}
\indexentry{natural number ! definition of|hyperpage}{4}
\indexentry{integer ! set of|hyperpage}{4}
\indexentry{integer ! definition of|hyperpage}{4}
\indexentry{rational number ! set of|hyperpage}{4}
\indexentry{rational number ! definition of|hyperpage}{4}
\indexentry{real number ! set of|hyperpage}{4}
\indexentry{real number ! definition of|hyperpage}{4}
\indexentry{irrational number ! set of|hyperpage}{4}
\indexentry{irrational number ! definition of|hyperpage}{4}
\indexentry{complex number ! set of|hyperpage}{4}
\indexentry{complex number ! definition of|hyperpage}{4}
\indexentry{trichotomy|hyperpage}{6}
\indexentry{interval ! definition of|hyperpage}{6}
\indexentry{interval ! notation for|hyperpage}{6}
\indexentry{relatively prime|hyperpage}{13}
\indexentry{base|hyperpage}{17}
\indexentry{exponent|hyperpage}{17}
\indexentry{$n^{\text  {th}}$ root ! principal|hyperpage}{20}
\indexentry{principal $n^{\text  {th}}$ root|hyperpage}{20}
\indexentry{root ! index|hyperpage}{20}
\indexentry{index of a root|hyperpage}{20}
\indexentry{root ! radicand|hyperpage}{20}
\indexentry{radicand|hyperpage}{20}
\indexentry{radical ! properties of|hyperpage}{21}
\indexentry{product rule ! for radicals|hyperpage}{21}
\indexentry{quotient rule ! for radicals|hyperpage}{21}
\indexentry{power rule ! for radicals|hyperpage}{21}
\indexentry{rational exponent|hyperpage}{21}
\indexentry{Cartesian coordinate plane|hyperpage}{27}
\indexentry{$x$-axis|hyperpage}{27}
\indexentry{$y$-axis|hyperpage}{27}
\indexentry{ordered pair|hyperpage}{27}
\indexentry{abscissa|hyperpage}{27}
\indexentry{$x$-coordinate|hyperpage}{27}
\indexentry{ordinate|hyperpage}{27}
\indexentry{$y$-coordinate|hyperpage}{27}
\indexentry{coordinates ! Cartesian|hyperpage}{27}
\indexentry{Cartesian coordinates|hyperpage}{27}
\indexentry{origin|hyperpage}{27}
\indexentry{quadrants|hyperpage}{29}
\indexentry{symmetry ! about the $x$-axis|hyperpage}{29}
\indexentry{symmetry ! about the $y$-axis|hyperpage}{29}
\indexentry{symmetry ! about the origin|hyperpage}{29}
\indexentry{reflection ! of a point|hyperpage}{30}
\indexentry{distance ! definition|hyperpage}{30}
\indexentry{distance ! distance formula|hyperpage}{31}
\indexentry{midpoint ! definition of|hyperpage}{32}
\indexentry{midpoint ! midpoint formula|hyperpage}{32}
\indexentry{numbers ! complex|hyperpage}{35}
\indexentry{complex numbers|hyperpage}{35}
\indexentry{imaginary unit, $i$|hyperpage}{35}
\indexentry{complex number ! imaginary unit, $i$|hyperpage}{35}
\indexentry{complex number ! definition of|hyperpage}{35}
\indexentry{complex number ! complex conjugate ! definition of|hyperpage}{37}
\indexentry{conjugate ! complex conjugate ! definition of|hyperpage}{37}
\indexentry{complex number ! conjugate ! properties of|hyperpage}{37}
\indexentry{conjugate of a complex number ! properties of|hyperpage}{37}
\indexentry{relation ! definition|hyperpage}{43}
\indexentry{graph ! of a relation|hyperpage}{43}
\indexentry{relation ! algebraic description|hyperpage}{44}
\indexentry{line ! vertical|hyperpage}{45}
\indexentry{vertical line|hyperpage}{45}
\indexentry{line ! horizontal|hyperpage}{45}
\indexentry{horizontal line|hyperpage}{45}
\indexentry{equation ! graph of|hyperpage}{45}
\indexentry{graph ! of an equation|hyperpage}{45}
\indexentry{Fundamental Graphing Principle ! for equations|hyperpage}{45}
\indexentry{relation ! Fundamental Graphing Principle|hyperpage}{45}
\indexentry{intercept ! definition of|hyperpage}{46}
\indexentry{$x$-intercept|hyperpage}{46}
\indexentry{$y$-intercept|hyperpage}{46}
\indexentry{intercept ! location of|hyperpage}{47}
\indexentry{symmetry ! testing an equation for|hyperpage}{47}
\indexentry{function ! definition as a relation|hyperpage}{53}
\indexentry{Vertical Line Test (VLT)|hyperpage}{53}
\indexentry{function ! domain|hyperpage}{55}
\indexentry{domain ! definition of|hyperpage}{55}
\indexentry{function ! range|hyperpage}{55}
\indexentry{range ! definition of|hyperpage}{55}
\indexentry{projection ! $x-$axis|hyperpage}{55}
\indexentry{projection ! $y-$axis|hyperpage}{55}
\indexentry{function ! as a process|hyperpage}{60}
\indexentry{function ! notation|hyperpage}{60}
\indexentry{variable ! independent|hyperpage}{60}
\indexentry{independent variable|hyperpage}{60}
\indexentry{function ! independent variable of|hyperpage}{60}
\indexentry{function ! argument|hyperpage}{60}
\indexentry{argument ! of a function|hyperpage}{60}
\indexentry{variable ! dependent|hyperpage}{60}
\indexentry{dependent variable|hyperpage}{60}
\indexentry{function ! dependent variable of|hyperpage}{60}
\indexentry{domain ! implied|hyperpage}{62}
\indexentry{implied domain of a function|hyperpage}{62}
\indexentry{mathematical model|hyperpage}{64}
\indexentry{model ! mathematical|hyperpage}{64}
\indexentry{domain ! applied|hyperpage}{64}
\indexentry{applied domain of a function|hyperpage}{64}
\indexentry{function ! piecewise-defined|hyperpage}{66}
\indexentry{piecewise-defined function|hyperpage}{66}
\indexentry{integer ! greatest integer function|hyperpage}{69}
\indexentry{greatest integer function|hyperpage}{69}
\indexentry{function ! arithmetic|hyperpage}{70}
\indexentry{function ! sum|hyperpage}{70}
\indexentry{function ! difference|hyperpage}{70}
\indexentry{function ! product|hyperpage}{70}
\indexentry{function ! quotient|hyperpage}{70}
\indexentry{function ! difference quotient|hyperpage}{72}
\indexentry{difference quotient|hyperpage}{72}
\indexentry{price-demand function|hyperpage}{75}
\indexentry{function ! price-demand|hyperpage}{75}
\indexentry{revenue function|hyperpage}{75}
\indexentry{function ! revenue|hyperpage}{75}
\indexentry{cost function|hyperpage}{75}
\indexentry{function ! cost|hyperpage}{75}
\indexentry{cost ! fixed, start-up|hyperpage}{75}
\indexentry{fixed cost|hyperpage}{75}
\indexentry{start-up cost|hyperpage}{75}
\indexentry{average cost function|hyperpage}{75}
\indexentry{cost ! average|hyperpage}{75}
\indexentry{function ! average cost|hyperpage}{75}
\indexentry{profit function|hyperpage}{75}
\indexentry{function ! profit|hyperpage}{75}
\indexentry{function ! Fundamental Graphing Principle|hyperpage}{80}
\indexentry{graph ! of a function|hyperpage}{80}
\indexentry{Fundamental Graphing Principle ! for functions|hyperpage}{80}
\indexentry{function ! zero|hyperpage}{81}
\indexentry{zero ! of a function|hyperpage}{81}
\indexentry{symmetry ! testing a function graph for|hyperpage}{81}
\indexentry{function ! even|hyperpage}{82}
\indexentry{even function|hyperpage}{82}
\indexentry{function ! odd|hyperpage}{82}
\indexentry{odd function|hyperpage}{82}
\indexentry{increasing function ! intuitive definition of|hyperpage}{85}
\indexentry{decreasing function ! intuitive definition of|hyperpage}{85}
\indexentry{constant function ! intuitive definition of|hyperpage}{85}
\indexentry{function ! increasing|hyperpage}{85}
\indexentry{function ! decreasing|hyperpage}{85}
\indexentry{function ! constant|hyperpage}{85}
\indexentry{increasing function ! formal definition of|hyperpage}{85}
\indexentry{decreasing function ! formal definition of|hyperpage}{85}
\indexentry{constant function ! formal definition of|hyperpage}{85}
\indexentry{function ! local (relative) maximum|hyperpage}{86}
\indexentry{local maximum ! intuitive definition of|hyperpage}{86}
\indexentry{function ! local (relative) minimum|hyperpage}{86}
\indexentry{local minimum ! intuitive definition of|hyperpage}{86}
\indexentry{function ! (absolute) maximum|hyperpage}{86}
\indexentry{maximum ! intuitive definition of|hyperpage}{86}
\indexentry{function ! (absolute, global) minimum|hyperpage}{86}
\indexentry{minimum ! intuitive definition of|hyperpage}{86}
\indexentry{local maximum ! formal definition of|hyperpage}{86}
\indexentry{local minimum ! formal definition of|hyperpage}{86}
\indexentry{maximum ! formal definition of|hyperpage}{86}
\indexentry{minimum ! formal definition of|hyperpage}{86}
\indexentry{transformations of function graphs|hyperpage}{94}
\indexentry{function ! transformation of graphs|hyperpage}{94}
\indexentry{graph ! vertical shift|hyperpage}{95}
\indexentry{graph ! horizontal shift|hyperpage}{96}
\indexentry{graph ! reflection about an axis|hyperpage}{98}
\indexentry{reflection ! of a function graph|hyperpage}{98}
\indexentry{transformation ! rigid|hyperpage}{100}
\indexentry{transformation ! non-rigid|hyperpage}{100}
\indexentry{graph ! vertical scaling|hyperpage}{101}
\indexentry{graph ! horizontal scaling|hyperpage}{102}
\indexentry{transformations of function graphs|hyperpage}{104}
\indexentry{function ! transformation of graphs|hyperpage}{104}
\indexentry{graph ! transformations|hyperpage}{104}
\indexentry{slope ! definition|hyperpage}{111}
\indexentry{line ! slope of|hyperpage}{111}
\indexentry{slope ! of a line|hyperpage}{111}
\indexentry{slope ! rate of change|hyperpage}{113}
\indexentry{rate of change ! slope of a line|hyperpage}{113}
\indexentry{line ! point-slope form|hyperpage}{114}
\indexentry{point-slope form of a line|hyperpage}{114}
\indexentry{line ! slope-intercept form|hyperpage}{114}
\indexentry{slope-intercept form of a line|hyperpage}{114}
\indexentry{function ! linear|hyperpage}{115}
\indexentry{line ! linear function|hyperpage}{115}
\indexentry{linear function|hyperpage}{115}
\indexentry{function ! constant|hyperpage}{115}
\indexentry{constant function ! as a horizontal line|hyperpage}{115}
\indexentry{cost ! variable|hyperpage}{117}
\indexentry{variable cost|hyperpage}{117}
\indexentry{average rate of change|hyperpage}{119}
\indexentry{rate of change ! average|hyperpage}{119}
\indexentry{secant line|hyperpage}{119}
\indexentry{rate of change ! instantaneous|hyperpage}{119}
\indexentry{instantaneous rate of change|hyperpage}{119}
\indexentry{line ! parallel|hyperpage}{123}
\indexentry{line ! perpendicular|hyperpage}{123}
\indexentry{function ! identity|hyperpage}{123}
\indexentry{absolute value ! definition of|hyperpage}{124}
\indexentry{function ! absolute value|hyperpage}{124}
\indexentry{absolute value ! properties of|hyperpage}{124}
\indexentry{product rule ! for absolute value|hyperpage}{124}
\indexentry{power rule ! for absolute value|hyperpage}{124}
\indexentry{quotient rule ! for absolute value|hyperpage}{124}
\indexentry{Triangle Inequality|hyperpage}{132}
\indexentry{function ! quadratic|hyperpage}{133}
\indexentry{quadratic function ! definition of|hyperpage}{133}
\indexentry{parabola ! graph of a quadratic function|hyperpage}{133}
\indexentry{parabola ! vertex|hyperpage}{133}
\indexentry{vertex ! of a parabola|hyperpage}{133}
\indexentry{quadratic function ! general form|hyperpage}{134}
\indexentry{quadratic function ! standard form|hyperpage}{134}
\indexentry{parabola ! axis of symmetry|hyperpage}{135}
\indexentry{axis of symmetry|hyperpage}{135}
\indexentry{parabola ! vertex formulas|hyperpage}{137}
\indexentry{quadratic formula|hyperpage}{137}
\indexentry{discriminant ! of a quadratic equation|hyperpage}{138}
\indexentry{discriminant ! trichotomy|hyperpage}{139}
\indexentry{inequality ! graphical interpretation|hyperpage}{146}
\indexentry{inequality ! absolute value|hyperpage}{147}
\indexentry{absolute value ! inequality|hyperpage}{147}
\indexentry{inequality ! sign diagram|hyperpage}{148}
\indexentry{sign diagram ! for quadratic inequality|hyperpage}{148}
\indexentry{inequality ! quadratic|hyperpage}{149}
\indexentry{quadratic function ! inequality|hyperpage}{149}
\indexentry{function ! polynomial|hyperpage}{155}
\indexentry{polynomial function ! definition of|hyperpage}{155}
\indexentry{polynomial function ! degree|hyperpage}{156}
\indexentry{degree of a polynomial|hyperpage}{156}
\indexentry{polynomial function ! leading term|hyperpage}{156}
\indexentry{leading term of a polynomial|hyperpage}{156}
\indexentry{polynomial function ! leading coefficient|hyperpage}{156}
\indexentry{leading coefficient of a polynomial|hyperpage}{156}
\indexentry{polynomial function ! constant term|hyperpage}{156}
\indexentry{constant term of a polynomial|hyperpage}{156}
\indexentry{polynomial function ! end behaviour|hyperpage}{158}
\indexentry{end behaviour ! of a function graph|hyperpage}{158}
\indexentry{end behaviour ! of $f(x) = ax^{n}, n$ even|hyperpage}{159}
\indexentry{end behaviour ! of $f(x) = ax^{n}, n$ odd|hyperpage}{159}
\indexentry{continuous|hyperpage}{159}
\indexentry{function ! continuous|hyperpage}{159}
\indexentry{smooth|hyperpage}{159}
\indexentry{function ! smooth|hyperpage}{159}
\indexentry{Intermediate Value Theorem ! polynomial zero version|hyperpage}{160}
\indexentry{sign diagram ! polynomial function|hyperpage}{161}
\indexentry{end behaviour ! polynomial|hyperpage}{161}
\indexentry{polynomial function ! zero ! multiplicity|hyperpage}{163}
\indexentry{multiplicity ! of a zero|hyperpage}{163}
\indexentry{zero ! multiplicity of|hyperpage}{163}
\indexentry{multiplicity ! effect on the graph of a polynomial|hyperpage}{163}
\indexentry{multiplicity ! effect on the graph of a polynomial|hyperpage}{165}
\indexentry{polynomial division ! dividend|hyperpage}{166}
\indexentry{polynomial division ! divisor|hyperpage}{166}
\indexentry{polynomial division ! quotient|hyperpage}{166}
\indexentry{polynomial division ! remainder|hyperpage}{166}
\indexentry{polynomial division ! factor|hyperpage}{166}
\indexentry{Remainder Theorem|hyperpage}{167}
\indexentry{Factor Theorem|hyperpage}{167}
\indexentry{Cauchy's Bound|hyperpage}{171}
\indexentry{Rational Zeros Theorem|hyperpage}{171}
\indexentry{$u$-substitution|hyperpage}{174}
\indexentry{Bisection Method|hyperpage}{176}
\indexentry{Fundamental Theorem of Algebra|hyperpage}{181}
\indexentry{Fundamental Theorem of Algebra|hyperpage}{181}
\indexentry{theorem ! Fundamental Theorem of Algebra|hyperpage}{181}
\indexentry{Complex Factorization Theorem|hyperpage}{182}
\indexentry{factorization ! over the complex numbers|hyperpage}{182}
\indexentry{polynomial function ! completely factored ! over the complex numbers|hyperpage}{183}
\indexentry{polynomial function ! completely factored ! over the real numbers|hyperpage}{183}
\indexentry{quadratic function ! irreducible quadratic|hyperpage}{183}
\indexentry{irreducible quadratic|hyperpage}{183}
\indexentry{Conjugate Pairs Theorem|hyperpage}{183}
\indexentry{Real Factorization Theorem|hyperpage}{184}
\indexentry{rational functions|hyperpage}{189}
\indexentry{function ! rational|hyperpage}{189}
\indexentry{asymptote ! vertical ! intuitive definition of|hyperpage}{191}
\indexentry{vertical asymptote ! intuitive definition of|hyperpage}{191}
\indexentry{asymptote ! horizontal ! intuitive definition of|hyperpage}{191}
\indexentry{horizontal asymptote ! intuitive definition of|hyperpage}{191}
\indexentry{asymptote ! vertical ! formal definition of|hyperpage}{191}
\indexentry{vertical asymptote ! formal definition of|hyperpage}{191}
\indexentry{asymptote ! horizontal ! formal definition of|hyperpage}{191}
\indexentry{horizontal asymptote ! formal definition of|hyperpage}{191}
\indexentry{hole ! in a graph|hyperpage}{192}
\indexentry{graph ! hole in|hyperpage}{192}
\indexentry{hole ! location of|hyperpage}{192}
\indexentry{asymptote ! vertical ! location of|hyperpage}{192}
\indexentry{vertical asymptote ! location of|hyperpage}{192}
\indexentry{asymptote ! horizontal ! location of|hyperpage}{195}
\indexentry{horizontal asymptote ! location of|hyperpage}{195}
\indexentry{asymptote ! slant (oblique)|hyperpage}{197}
\indexentry{slant asymptote|hyperpage}{197}
\indexentry{oblique asymptote|hyperpage}{197}
\indexentry{asymptote ! slant ! formal definition of|hyperpage}{197}
\indexentry{slant asymptote ! formal definition of|hyperpage}{197}
\indexentry{asymptote ! slant ! determination of|hyperpage}{198}
\indexentry{slant asymptote ! determination of|hyperpage}{198}
\indexentry{interrobang|hyperpage}{201}
\indexentry{sign diagram ! rational function|hyperpage}{202}
\indexentry{graph ! rational function|hyperpage}{202}
\indexentry{cost ! average|hyperpage}{215}
\indexentry{average cost|hyperpage}{215}
\indexentry{variation ! direct|hyperpage}{218}
\indexentry{direct variation|hyperpage}{218}
\indexentry{variation ! inverse|hyperpage}{218}
\indexentry{inverse variation|hyperpage}{218}
\indexentry{variation ! joint|hyperpage}{218}
\indexentry{joint variation|hyperpage}{218}
\indexentry{variation ! constant of proportionality|hyperpage}{218}
\indexentry{constant of proportionality|hyperpage}{218}
\indexentry{Hooke's Law|hyperpage}{218}
\indexentry{Boyle's Law|hyperpage}{218}
\indexentry{Ohm's Law|hyperpage}{218}
\indexentry{Newton's Law of Universal Gravitation|hyperpage}{218}
\indexentry{Charles's Law|hyperpage}{221}
\indexentry{Kepler's Third Law of Planetary Motion|hyperpage}{221}
\indexentry{Coulomb's Law|hyperpage}{221}
\indexentry{BMI, body mass index|hyperpage}{221}
\indexentry{function ! composite ! definition of|hyperpage}{223}
\indexentry{composite function ! definition of|hyperpage}{223}
\indexentry{commutative property ! function composition does not have|hyperpage}{229}
\indexentry{associative property ! for function composition|hyperpage}{229}
\indexentry{function ! composite ! properties of|hyperpage}{229}
\indexentry{composite function ! properties of|hyperpage}{229}
\indexentry{identity ! function|hyperpage}{230}
\indexentry{function ! as a process|hyperpage}{234}
\indexentry{function ! inverse ! definition of|hyperpage}{234}
\indexentry{inverse ! of a function ! definition of|hyperpage}{234}
\indexentry{invertible ! function|hyperpage}{234}
\indexentry{inverse ! of a function ! properties of|hyperpage}{235}
\indexentry{function ! inverse ! properties of|hyperpage}{235}
\indexentry{inverse ! of a function ! uniqueness of|hyperpage}{235}
\indexentry{function ! inverse ! uniqueness of|hyperpage}{235}
\indexentry{function ! one-to-one|hyperpage}{236}
\indexentry{one-to-one function|hyperpage}{236}
\indexentry{Horizontal Line Test (HLT)|hyperpage}{236}
\indexentry{invertibility ! function|hyperpage}{237}
\indexentry{inverse ! of a function ! solving for|hyperpage}{239}
\indexentry{function ! inverse ! solving for|hyperpage}{239}
\indexentry{$n^{\textrm  {th}}$ root ! principal|hyperpage}{246}
\indexentry{principal $n^{\textrm  {th}}$ root|hyperpage}{246}
\indexentry{root ! index|hyperpage}{246}
\indexentry{index of a root|hyperpage}{246}
\indexentry{root ! radicand|hyperpage}{246}
\indexentry{radicand|hyperpage}{246}
\indexentry{radical ! properties of|hyperpage}{246}
\indexentry{product rule ! for radicals|hyperpage}{246}
\indexentry{power rule ! for radicals|hyperpage}{246}
\indexentry{quotient rule ! for radicals|hyperpage}{246}
\indexentry{rational exponent|hyperpage}{247}
\indexentry{function ! algebraic|hyperpage}{247}
\indexentry{sign diagram ! algebraic function|hyperpage}{248}
\indexentry{function ! exponential|hyperpage}{258}
\indexentry{exponential function ! definition of|hyperpage}{258}
\indexentry{exponential function ! graphical properties of|hyperpage}{259}
\indexentry{exponential function ! common base|hyperpage}{259}
\indexentry{common base|hyperpage}{259}
\indexentry{natural base|hyperpage}{259}
\indexentry{exponential function ! natural base|hyperpage}{259}
\indexentry{depreciation|hyperpage}{259}
\indexentry{Newton's Law of Cooling|hyperpage}{260}
\indexentry{function ! logarithmic|hyperpage}{261}
\indexentry{logarithm ! general, ``base $b$''|hyperpage}{261}
\indexentry{logarithm ! common|hyperpage}{261}
\indexentry{logarithm ! natural|hyperpage}{261}
\indexentry{common logarithm|hyperpage}{261}
\indexentry{natural logarithm|hyperpage}{261}
\indexentry{logarithm ! graphical properties of|hyperpage}{262}
\indexentry{argument ! of a logarithm|hyperpage}{264}
\indexentry{logarithmic scales|hyperpage}{268}
\indexentry{Richter Scale|hyperpage}{268}
\indexentry{earthquake ! Richter Scale|hyperpage}{268}
\indexentry{decibel|hyperpage}{268}
\indexentry{sound intensity level ! decibel|hyperpage}{268}
\indexentry{pH|hyperpage}{269}
\indexentry{acidity of a solution ! pH|hyperpage}{269}
\indexentry{alkalinity of a solution ! pH|hyperpage}{269}
\indexentry{exponential function ! inverse properties of|hyperpage}{270}
\indexentry{logarithm ! inverse properties of|hyperpage}{270}
\indexentry{exponential function ! one-to-one properties of|hyperpage}{270}
\indexentry{logarithm ! one-to-one properties of|hyperpage}{270}
\indexentry{exponential function ! algebraic properties of|hyperpage}{271}
\indexentry{product rule ! for exponential functions|hyperpage}{271}
\indexentry{quotient rule ! for exponential functions|hyperpage}{271}
\indexentry{power rule ! for exponential functions|hyperpage}{271}
\indexentry{logarithm ! algebraic properties of|hyperpage}{271}
\indexentry{product rule ! for logarithms|hyperpage}{271}
\indexentry{quotient rule ! for logarithms|hyperpage}{271}
\indexentry{power rule ! for logarithms|hyperpage}{271}
\indexentry{change of base formulas|hyperpage}{275}
\indexentry{exponential function ! change of base formula|hyperpage}{275}
\indexentry{logarithm ! change of base formula|hyperpage}{275}
\indexentry{Henderson-Hasselbalch Equation|hyperpage}{278}
\indexentry{exponential function ! solving equations with|hyperpage}{279}
\indexentry{logarithm ! solving equations with|hyperpage}{287}
\indexentry{interest ! simple|hyperpage}{294}
\indexentry{simple interest|hyperpage}{294}
\indexentry{principal|hyperpage}{294}
\indexentry{interest ! compound|hyperpage}{295}
\indexentry{compound interest|hyperpage}{295}
\indexentry{interest ! compounded continuously|hyperpage}{297}
\indexentry{continuously compounded interest|hyperpage}{297}
\indexentry{instantaneous rate of change|hyperpage}{297}
\indexentry{rate of change ! instantaneous|hyperpage}{297}
\indexentry{growth model ! uninhibited|hyperpage}{297}
\indexentry{uninhibited growth|hyperpage}{297}
\indexentry{radioactive decay|hyperpage}{298}
\indexentry{Newton's Law of Cooling|hyperpage}{299}
\indexentry{growth model ! limited|hyperpage}{300}
\indexentry{growth model ! logistic|hyperpage}{300}
\indexentry{logistic growth|hyperpage}{300}
\indexentry{inflection point|hyperpage}{301}
\indexentry{point of diminishing returns|hyperpage}{301}
\indexentry{password strength|hyperpage}{302}
\indexentry{information entropy|hyperpage}{302}
\indexentry{buffer solution|hyperpage}{302}
\indexentry{ray ! definition of|hyperpage}{307}
\indexentry{ray ! initial point|hyperpage}{307}
\indexentry{angle ! definition|hyperpage}{307}
\indexentry{angle ! vertex|hyperpage}{307}
\indexentry{vertex ! of an angle|hyperpage}{307}
\indexentry{angle ! straight|hyperpage}{307}
\indexentry{straight angle|hyperpage}{307}
\indexentry{angle ! measurement|hyperpage}{307}
\indexentry{measure of an angle|hyperpage}{307}
\indexentry{angle ! degree|hyperpage}{307}
\indexentry{degree measure|hyperpage}{307}
\indexentry{right angle|hyperpage}{307}
\indexentry{angle ! right|hyperpage}{307}
\indexentry{acute angle|hyperpage}{308}
\indexentry{angle ! acute|hyperpage}{308}
\indexentry{obtuse angle|hyperpage}{308}
\indexentry{angle ! obtuse|hyperpage}{308}
\indexentry{complementary angles|hyperpage}{308}
\indexentry{angle ! complementary|hyperpage}{308}
\indexentry{supplementary angles|hyperpage}{308}
\indexentry{angle ! supplementary|hyperpage}{308}
\indexentry{angle ! oriented|hyperpage}{308}
\indexentry{oriented angle|hyperpage}{308}
\indexentry{angle ! initial side|hyperpage}{308}
\indexentry{initial side of an angle|hyperpage}{308}
\indexentry{angle ! terminal side|hyperpage}{308}
\indexentry{terminal side of an angle|hyperpage}{308}
\indexentry{angle ! positive|hyperpage}{308}
\indexentry{positive angle|hyperpage}{308}
\indexentry{angle ! negative|hyperpage}{308}
\indexentry{negative angle|hyperpage}{308}
\indexentry{angle ! standard position|hyperpage}{309}
\indexentry{standard position of an angle|hyperpage}{309}
\indexentry{angle ! quadrantal|hyperpage}{309}
\indexentry{quadrantal angle|hyperpage}{309}
\indexentry{angle ! coterminal|hyperpage}{309}
\indexentry{coterminal angle|hyperpage}{309}
\indexentry{pi, ${"π}$|hyperpage}{310}
\indexentry{angle ! central angle|hyperpage}{310}
\indexentry{central angle|hyperpage}{310}
\indexentry{angle ! radian measure|hyperpage}{310}
\indexentry{radian measure|hyperpage}{310}
\indexentry{wrapping function|hyperpage}{312}
\indexentry{oriented arc|hyperpage}{312}
\indexentry{velocity ! average angular|hyperpage}{314}
\indexentry{average angular velocity|hyperpage}{314}
\indexentry{frequency ! ordinary|hyperpage}{314}
\indexentry{ordinary frequency|hyperpage}{314}
\indexentry{frequency ! angular|hyperpage}{315}
\indexentry{angular frequency|hyperpage}{315}
\indexentry{period ! circular motion|hyperpage}{315}
\indexentry{cosine ! of an angle|hyperpage}{318}
\indexentry{sine ! of an angle|hyperpage}{318}
\indexentry{angle ! reference|hyperpage}{321}
\indexentry{reference angle|hyperpage}{321}
\indexentry{Reference Angle Theorem ! for cosine and sine|hyperpage}{322}
\indexentry{Unit Circle ! important points|hyperpage}{323}
\indexentry{cosine ! of an angle|hyperpage}{329}
\indexentry{sine ! of an angle|hyperpage}{329}
\indexentry{circular function|hyperpage}{336}
\indexentry{function ! circular|hyperpage}{336}
\indexentry{cosine ! of an angle|hyperpage}{336}
\indexentry{sine ! of an angle|hyperpage}{336}
\indexentry{secant ! of an angle|hyperpage}{336}
\indexentry{cosecant ! of an angle|hyperpage}{336}
\indexentry{tangent ! of an angle|hyperpage}{336}
\indexentry{cotangent ! of an angle|hyperpage}{336}
\indexentry{Reciprocal Identities|hyperpage}{337}
\indexentry{Quotient Identities|hyperpage}{337}
\indexentry{Reference Angle Theorem ! for the circular functions|hyperpage}{338}
\indexentry{Pythagorean Identities|hyperpage}{340}
\indexentry{Pythagorean Conjugates|hyperpage}{342}
\indexentry{secant ! of an angle|hyperpage}{344}
\indexentry{cosecant ! of an angle|hyperpage}{344}
\indexentry{tangent ! of an angle|hyperpage}{344}
\indexentry{cotangent ! of an angle|hyperpage}{344}
\indexentry{angle ! of inclination|hyperpage}{345}
\indexentry{angle ! of elevation|hyperpage}{345}
\indexentry{extended interval notation|hyperpage}{347}
\indexentry{interval ! notation, extended|hyperpage}{347}
\indexentry{angle ! of depression|hyperpage}{351}
\indexentry{angle ! of declination|hyperpage}{351}
\indexentry{Even/Odd Identities|hyperpage}{354}
\indexentry{Difference Identity ! for cosine|hyperpage}{354}
\indexentry{Sum Identity ! for cosine|hyperpage}{354}
\indexentry{Cofunction Identities|hyperpage}{356}
\indexentry{Difference Identity ! for sine|hyperpage}{357}
\indexentry{Sum Identity ! for sine|hyperpage}{357}
\indexentry{Difference Identity ! for tangent|hyperpage}{359}
\indexentry{Sum Identity ! for tangent|hyperpage}{359}
\indexentry{Difference Identity ! for cosine|hyperpage}{359}
\indexentry{Sum Identity ! for cosine|hyperpage}{359}
\indexentry{Difference Identity ! for sine|hyperpage}{359}
\indexentry{Sum Identity ! for sine|hyperpage}{359}
\indexentry{Double Angle Identities|hyperpage}{359}
\indexentry{Power Reduction Formulas|hyperpage}{361}
\indexentry{Half-Angle Formulas|hyperpage}{362}
\indexentry{Product to Sum Formulas|hyperpage}{364}
\indexentry{Sum to Product Formulas|hyperpage}{364}
\indexentry{function ! periodic|hyperpage}{369}
\indexentry{periodic function|hyperpage}{369}
\indexentry{period ! of a function|hyperpage}{369}
\indexentry{cosine ! properties of|hyperpage}{370}
\indexentry{sine ! properties of|hyperpage}{370}
\indexentry{fundamental cycle ! of $y = \cos(x)$|hyperpage}{370}
\indexentry{cosine ! graph of|hyperpage}{370}
\indexentry{sine ! graph of|hyperpage}{370}
\indexentry{argument ! of a trigonometric function|hyperpage}{371}
\indexentry{amplitude|hyperpage}{372}
\indexentry{sinusoid ! amplitude|hyperpage}{372}
\indexentry{phase shift|hyperpage}{372}
\indexentry{sinusoid ! phase shift|hyperpage}{372}
\indexentry{sinusoid ! graph of|hyperpage}{372}
\indexentry{phase|hyperpage}{373}
\indexentry{frequency ! of a sinusoid|hyperpage}{373}
\indexentry{secant ! graph of|hyperpage}{376}
\indexentry{cosecant ! graph of|hyperpage}{377}
\indexentry{secant ! properties of|hyperpage}{379}
\indexentry{cosecant ! properties of|hyperpage}{379}
\indexentry{tangent ! graph of|hyperpage}{381}
\indexentry{cotangent ! graph of|hyperpage}{381}
\indexentry{tangent ! properties of|hyperpage}{383}
\indexentry{cotangent ! properties of|hyperpage}{383}
\indexentry{arccosine ! graph of|hyperpage}{387}
\indexentry{arcsine ! graph of|hyperpage}{387}
\indexentry{arccosine ! definition of|hyperpage}{388}
\indexentry{arccosine ! properties of|hyperpage}{388}
\indexentry{arcsine ! definition of|hyperpage}{388}
\indexentry{arcsine ! properties of|hyperpage}{388}
\indexentry{arctangent ! graph of|hyperpage}{390}
\indexentry{arccotangent ! graph of|hyperpage}{390}
\indexentry{arctangent ! definition of|hyperpage}{391}
\indexentry{arctangent ! properties of|hyperpage}{391}
\indexentry{arccotangent ! definition of|hyperpage}{391}
\indexentry{arccotangent ! properties of|hyperpage}{391}
\indexentry{arcsecant ! trigonometry friendly ! graph of|hyperpage}{393}
\indexentry{arccosecant ! trigonometry friendly ! graph of|hyperpage}{393}
\indexentry{arcsecant ! trigonometry friendly ! definition of|hyperpage}{394}
\indexentry{arcsecant ! trigonometry friendly ! properties of|hyperpage}{394}
\indexentry{arccosecant ! trigonometry friendly ! definition of|hyperpage}{394}
\indexentry{arccosecant ! trigonometry friendly ! properties of|hyperpage}{394}
\indexentry{arcsecant ! calculus friendly ! graph of|hyperpage}{396}
\indexentry{arccosecant ! calculus friendly ! graph of|hyperpage}{396}
\indexentry{arcsecant ! calculus friendly ! definition of|hyperpage}{396}
\indexentry{arcsecant ! calculus friendly ! properties of|hyperpage}{396}
\indexentry{arccosecant ! calculus friendly ! definition of|hyperpage}{396}
\indexentry{arccosecant ! calculus friendly ! properties of|hyperpage}{396}
\indexentry{sinusoid ! graph of|hyperpage}{427}
\indexentry{sinusoid ! properties of|hyperpage}{427}
\indexentry{sinusoid ! amplitude|hyperpage}{427}
\indexentry{amplitude|hyperpage}{427}
\indexentry{sinusoid ! frequency ! angular|hyperpage}{427}
\indexentry{frequency ! angular|hyperpage}{427}
\indexentry{sinusoid ! frequency ! ordinary|hyperpage}{427}
\indexentry{frequency ! ordinary|hyperpage}{427}
\indexentry{sinusoid ! period|hyperpage}{427}
\indexentry{period ! of a sinusoid|hyperpage}{427}
\indexentry{sinusoid ! phase|hyperpage}{427}
\indexentry{phase|hyperpage}{427}
\indexentry{sinusoid ! phase shift|hyperpage}{427}
\indexentry{phase shift|hyperpage}{427}
\indexentry{sinusoid ! vertical shift|hyperpage}{427}
\indexentry{sinusoid ! baseline|hyperpage}{427}
\indexentry{harmonic motion|hyperpage}{428}
\indexentry{angle side opposite pairs|hyperpage}{434}
\indexentry{Law of Sines|hyperpage}{435}
\indexentry{bearings|hyperpage}{442}
\indexentry{Side-Angle-Side triangle|hyperpage}{443}
\indexentry{Side-Side-Side triangle|hyperpage}{443}
\indexentry{Law of Cosines|hyperpage}{443}
\indexentry{Heron's Formula|hyperpage}{446}
\indexentry{rectangular coordinates ! also known as Cartesian coordinates|hyperpage}{451}
\indexentry{coordinates ! rectangular|hyperpage}{451}
\indexentry{polar coordinates ! definition of|hyperpage}{451}
\indexentry{coordinates ! polar|hyperpage}{451}
\indexentry{polar coordinates ! pole|hyperpage}{451}
\indexentry{polar coordinates ! polar axis|hyperpage}{451}
\indexentry{polar coordinates ! equivalent representations of|hyperpage}{456}
\indexentry{polar coordinates ! conversion into rectangular|hyperpage}{457}
\indexentry{rectangular coordinates ! conversion into polar|hyperpage}{457}
\indexentry{complex number ! definition of|hyperpage}{465}
\indexentry{complex number ! real part|hyperpage}{465}
\indexentry{real part of a complex number|hyperpage}{465}
\indexentry{imaginary part of a complex number|hyperpage}{465}
\indexentry{complex number ! imaginary part|hyperpage}{465}
\indexentry{real axis|hyperpage}{465}
\indexentry{imaginary axis|hyperpage}{465}
\indexentry{complex plane|hyperpage}{465}
\indexentry{complex number ! rectangular form|hyperpage}{465}
\indexentry{rectangular form of a complex number|hyperpage}{465}
\indexentry{complex number ! modulus ! definition of|hyperpage}{465}
\indexentry{modulus of a complex number ! definition of|hyperpage}{465}
\indexentry{complex number ! argument ! definition of|hyperpage}{465}
\indexentry{argument ! of a complex number ! definition of|hyperpage}{465}
\indexentry{complex number ! principal argument|hyperpage}{465}
\indexentry{principal argument of a complex number|hyperpage}{465}
\indexentry{complex number ! modulus ! properties of|hyperpage}{467}
\indexentry{modulus of a complex number ! properties of|hyperpage}{467}
\indexentry{product rule ! for the modulus of a complex number|hyperpage}{467}
\indexentry{power rule ! for the modulus of a complex number|hyperpage}{467}
\indexentry{quotient rule ! for the modulus of a complex number|hyperpage}{467}
\indexentry{complex number ! argument ! properties of|hyperpage}{469}
\indexentry{argument ! of a complex number ! properties of|hyperpage}{469}
\indexentry{cis($\theta$)|hyperpage}{469}
\indexentry{complex number ! polar form ! cis-notation|hyperpage}{470}
\indexentry{polar form of a complex number|hyperpage}{470}
\indexentry{product rule ! for complex numbers|hyperpage}{471}
\indexentry{DeMoivre's Theorem|hyperpage}{471}
\indexentry{power rule ! for complex numbers|hyperpage}{471}
\indexentry{quotient rule ! for complex numbers|hyperpage}{471}
\indexentry{$n^{\textrm  {th}}$ root ! of a complex number|hyperpage}{475}
\indexentry{complex number ! $n^{\textrm  {th}}$ root|hyperpage}{475}
\indexentry{$n^{\textrm  {th}}$ root ! of a complex number|hyperpage}{476}
\indexentry{complex number ! $n^{\textrm  {th}}$ root|hyperpage}{476}
\indexentry{$n^{\textrm  {th}}$ Roots of Unity|hyperpage}{479}
\indexentry{complex number ! $n^{\textrm  {th}}$ Roots of Unity|hyperpage}{479}
\indexentry{Roots of Unity|hyperpage}{479}
\indexentry{limit!indeterminate form|hyperpage}{481}
\indexentry{indeterminate form|hyperpage}{481}
\indexentry{limit!pseudo-definition|hyperpage}{482}
\indexentry{limit!does not exist|hyperpage}{483}
\indexentry{limit!difference quotient|hyperpage}{485}
\indexentry{limit!definition|hyperpage}{486}
\indexentry{limit!informal definition|hyperpage}{486}
\indexentry{limit!properties|hyperpage}{488}
\indexentry{limit!Squeeze Theorem|hyperpage}{491}
\indexentry{Squeeze Theorem|hyperpage}{491}
\indexentry{limit!one sided|hyperpage}{498}
\indexentry{limit!right handed|hyperpage}{498}
\indexentry{limit!left handed|hyperpage}{498}
\indexentry{limit!does not exist|hyperpage}{499}
\indexentry{continuous function|hyperpage}{504}
\indexentry{floor function|hyperpage}{504}
\indexentry{continuous function!properties|hyperpage}{506}
\indexentry{Intermediate Value Theorem|hyperpage}{507}
\indexentry{Bisection Method|hyperpage}{508}
\indexentry{limit!of infinity|hyperpage}{512}
\indexentry{asymptote!vertical|hyperpage}{513}
\indexentry{limit!indeterminate form|hyperpage}{514}
\indexentry{indeterminate form|hyperpage}{514}
\indexentry{limit!at infinity|hyperpage}{514}
\indexentry{asymptote!horizontal|hyperpage}{514}
\indexentry{derivative!at a point|hyperpage}{523}
\indexentry{differentiable|hyperpage}{523}
\indexentry{tangent line|hyperpage}{523}
\indexentry{derivative!tangent line|hyperpage}{523}
\indexentry{derivative!normal line|hyperpage}{525}
\indexentry{normal line|hyperpage}{525}
\indexentry{derivative!as a function|hyperpage}{527}
\indexentry{derivative!notation|hyperpage}{527}
\indexentry{derivative!interpretation|hyperpage}{533}
\indexentry{velocity|hyperpage}{534}
\indexentry{acceleration|hyperpage}{535}
\indexentry{derivative!motion|hyperpage}{535}
\indexentry{derivative!velocity|hyperpage}{535}
\indexentry{derivative!acceleration|hyperpage}{535}
\indexentry{derivative!Constant Rule|hyperpage}{539}
\indexentry{derivative!Power Rule|hyperpage}{539}
\indexentry{Power Rule!differentiation|hyperpage}{539}
\indexentry{derivative!basic rules|hyperpage}{539}
\indexentry{derivative!Sum/Difference Rule|hyperpage}{540}
\indexentry{Sum/Difference Rule!of derivatives|hyperpage}{540}
\indexentry{derivative!Constant Multiple Rule|hyperpage}{540}
\indexentry{Constant Multiple Rule!of derivatives|hyperpage}{540}
\indexentry{derivative!higher order|hyperpage}{541}
\indexentry{derivative!notation|hyperpage}{541}
\indexentry{derivative!higher order!interpretation|hyperpage}{542}
\indexentry{Power Rule!differentiation|hyperpage}{545}
\indexentry{derivative!Product Rule|hyperpage}{545}
\indexentry{derivative!Quotient Rule|hyperpage}{547}
\indexentry{Quotient Rule|hyperpage}{547}
\indexentry{derivative!trigonometric functions|hyperpage}{549}
\indexentry{derivative!Power Rule|hyperpage}{550}
\indexentry{Power Rule!differentiation|hyperpage}{550}
\indexentry{derivative!Chain Rule|hyperpage}{555}
\indexentry{Chain Rule|hyperpage}{555}
\indexentry{derivative!Generalized Power Rule|hyperpage}{555}
\indexentry{Generalized Power Rule|hyperpage}{555}
\indexentry{derivative!exponential functions|hyperpage}{559}
\indexentry{Chain Rule!notation|hyperpage}{559}
\indexentry{derivative!Chain Rule|hyperpage}{559}
\indexentry{extreme values|hyperpage}{563}
\indexentry{absolute minimum|hyperpage}{563}
\indexentry{minimum!absolute|hyperpage}{563}
\indexentry{absolute maximum|hyperpage}{563}
\indexentry{maximum!absolute|hyperpage}{563}
\indexentry{extrema!absolute|hyperpage}{563}
\indexentry{Extreme Value Theorem|hyperpage}{563}
\indexentry{minimum!relative/local|hyperpage}{564}
\indexentry{maximum!relative/local|hyperpage}{564}
\indexentry{extrema!relative|hyperpage}{564}
\indexentry{critical number|hyperpage}{565}
\indexentry{critical point|hyperpage}{565}
\indexentry{extrema!finding|hyperpage}{565}
\indexentry{increasing function|hyperpage}{570}
\indexentry{decreasing function|hyperpage}{570}
\indexentry{increasing function!strictly|hyperpage}{570}
\indexentry{decreasing function!strictly|hyperpage}{570}
\indexentry{increasing function!finding intervals|hyperpage}{571}
\indexentry{decreasing function!finding intervals|hyperpage}{571}
\indexentry{First Derivative Test|hyperpage}{573}
\indexentry{derivative!First Deriv. Test|hyperpage}{573}
\indexentry{extrema!and First Deriv. Test|hyperpage}{573}
\indexentry{maximum!and First Deriv. Test|hyperpage}{573}
\indexentry{minimum!and First Deriv. Test|hyperpage}{573}
\indexentry{concavity|hyperpage}{577}
\indexentry{concave up|hyperpage}{577}
\indexentry{concave down|hyperpage}{577}
\indexentry{concavity!test for|hyperpage}{577}
\indexentry{concavity!inflection point|hyperpage}{577}
\indexentry{point of inflection|hyperpage}{578}
\indexentry{inflection point|hyperpage}{578}
\indexentry{derivative!Second Deriv. Test|hyperpage}{580}
\indexentry{Second Derivative Test|hyperpage}{580}
\indexentry{extrema!and Second Deriv. Test|hyperpage}{580}
\indexentry{maximum!and Second Deriv. Test|hyperpage}{580}
\indexentry{minimum!and First Deriv. Test|hyperpage}{580}
\indexentry{curve sketching|hyperpage}{584}
\indexentry{antiderivative|hyperpage}{590}
\indexentry{indefinite integral|hyperpage}{590}
\indexentry{integration!indefinite|hyperpage}{590}
\indexentry{integration!notation|hyperpage}{591}
\indexentry{Constant Multiple Rule!of integration|hyperpage}{593}
\indexentry{integration!Sum/Difference Rule|hyperpage}{593}
\indexentry{Sum/Difference Rule!of integration|hyperpage}{593}
\indexentry{integration!Power Rule|hyperpage}{594}
\indexentry{Power Rule!integration|hyperpage}{594}
\indexentry{initial value problem|hyperpage}{594}