A2.20

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

A2.20.aGraph polynomial functions expressed symbolically, identifying zeros when suitable factorizations are available, and showing end behavior.A2.20.bGraph sine and cosine functions expressed symbolically, showing period, midline, and amplitude.A2.20.cGraph logarithmic functions expressed symbolically, showing intercepts and end behavior.A2.20.dGraph reciprocal functions expressed symbolically, identifying horizontal and vertical asymptotes.A2.20.eGraph square root and cube root functions expressed symbolically.A2.20.fCompare the graphs of inverse functions and the relationships between their key features, including but not limited to quadratic, square root, exponential, and logarithmic functions.
Khan Academy Resources
Intro to inverse functionsGraphs of polynomials: Challenge problemsZeros of polynomials & their graphsGraphs of polynomialsMidline, amplitude, and period reviewEnd behavior of polynomialsSymmetry of algebraic modelsRadical functions & their graphsPositive & negative intervals of polynomialsGraph sinusoidal functionsGraphs of logarithmic functionsAmplitude of sinusoidal functions from equationGraph sinusoidal functions: phase shiftPeriod of sinusoidal functions from equationGraphs of square and cube root functionsGraphs of exponential functionsEnd behavior of polynomialsPeriodicity of algebraic modelsZeros of polynomials (with factoring)Inverse functions: graphs and tablesEnd behavior of algebraic modelsPositive & negative intervals of polynomialsEvaluate inverse functionsZeros of polynomials (multiplicity)Amplitude 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 contextGraph of y=sin(x)Intersection 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 inverse functionsTransforming exponential graphsPeriodicity of algebraic modelsGraphing the inverse of a linear functionFeatures of sinusoidal functionsZeros of polynomials (with factoring): groupingMultiplicity of zeros of polynomialsEnd behavior of algebraic modelsSymmetry of algebraic modelsZeros of polynomials: matching equation to graphGraphing logarithmic functions (example 1)Example: Graphing y=3⋅sin(½⋅x)-2Example: Graphing y=-cos(π⋅x)+1.5Zeros of polynomials: matching equation to zerosTransforming exponential graphs (example 2)Vertex form introductionGraph of y=tan(x)Graphing square and cube root functionsReading inverse values from a graphGraphing exponential functionsZeros of polynomials: plotting zerosIntro to end behavior of polynomialsReading inverse values from a tableInputs & outputs of inverse functionsGraphical relationship between 2ˣ and log₂(x)Zeros of polynomials (with factoring): common factorZeros of polynomials (multiplicity)Zeros of polynomials introductionGraphing logarithmic functions (example 2)
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