PC.2.I
Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing.
Khan Academy ResourcesZeros of polynomials & their graphsMidline, amplitude, and period reviewPositive & negative intervals of polynomialsGraph sinusoidal functionsAmplitude of sinusoidal functions from equationGraph sinusoidal functions: phase shiftGraphs of rational functionsRational functions: zeros, asymptotes, and undefined pointsConstruct sinusoidal functionsAverage rate of change of polynomialsPeriod of sinusoidal functions from equationGraphs of exponential functionsPeriodicity of algebraic modelsZeros of polynomials (with factoring)Positive & negative intervals of polynomialsZeros of polynomials (multiplicity)Solving equations graphically: word problemsAmplitude of sinusoidal functions from graphMidline of sinusoidal functions from equationZeros of polynomials (factored form)Period of sinusoidal functions from graphMidline of sinusoidal functions from graphInterpreting trigonometric graphs in contextIntersection points of y=sin(x) and y=cos(x)Amplitude & period of sinusoidal functions from equationTransforming sinusoidal graphs: vertical & horizontal stretchesTransforming sinusoidal graphs: vertical stretch & horizontal reflectionIntro to arcsineIntro to arctangentIntro to arccosineGraphing rational functions according to asymptotesGraphs of rational functions: horizontal asymptotePeriodicity of algebraic modelsPositive and negative intervals of polynomialsTangent identities: symmetryFeatures of sinusoidal functionsZeros of polynomials (with factoring): groupingMultiplicity of zeros of polynomialsEnd behavior of rational functionsZeros of polynomials: matching equation to graphExample: Graphing y=3⋅sin(½⋅x)-2Graphs of rational functions: zerosExample: Graphing y=-cos(π⋅x)+1.5Zeros of polynomials: matching equation to zerosSign of average rate of change of polynomialsGraphing exponential functionsZeros of polynomials: plotting zerosFinding average rate of change of polynomialsSine & cosine identities: symmetryInterpreting trigonometric graphs in contextGraphs of rational functions: y-interceptDiscontinuities of rational functionsGraphs of rational functions: vertical asymptotesSinusoidal function from graphZeros of polynomials (with factoring): common factorZeros of polynomials (multiplicity)Zeros of polynomials introduction

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