PC.26

Graph functions expressed symbolically and show key features of the graph, by hand and using technology. Use the equation of functions to identify key features in order to generate a graph.

PC.26.aGraph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.PC.26.bGraph trigonometric functions and their inverses, showing period, midline, amplitude, and phase shift.
Khan Academy Resources
Graphs of polynomials: Challenge problemsZeros of polynomials & their graphsGraphs of polynomialsMidline, amplitude, and period reviewPositive & negative intervals of polynomialsGraph sinusoidal functionsEnd behavior of rational functionsGraphs of logarithmic functionsAmplitude of sinusoidal functions from equationGraph sinusoidal functions: phase shiftGraphs of rational functionsRational functions: zeros, asymptotes, and undefined pointsPeriod of sinusoidal functions from equationGraphs of exponential functionsZeros of polynomials (with factoring)Positive & negative intervals of polynomialsZeros 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 reflectionGraphing rational functions according to asymptotesTransforming exponential graphsGraphs of rational functions: horizontal asymptoteFeatures of sinusoidal functionsZeros of polynomials (with factoring): groupingMultiplicity of zeros of polynomialsEnd behavior of rational functionsZeros of polynomials: matching equation to graphGraphing logarithmic functions (example 1)Example: Graphing y=3⋅sin(½⋅x)-2Graphs of rational functions: zerosExample: Graphing y=-cos(π⋅x)+1.5Zeros of polynomials: matching equation to zerosTransforming exponential graphs (example 2)Graph of y=tan(x)Graphing exponential functionsZeros of polynomials: plotting zerosGraphs of rational functions: y-interceptDiscontinuities of rational functionsGraphs of rational functions: vertical asymptotesGraphical 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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