AT.A.1.a
Analyze and graph nonlinear functions (trigonometric, rational, higher-order polynomials, logarithmic, and piecewise) and relations (conic sections) using their points of interest and graphing technology.
Example Problems
Evaluate:
Evaluate:
Evaluate:
Khan Academy ResourcesEllipse equation reviewEllipse foci reviewGraphs of polynomials: Challenge problemsZeros of polynomials & their graphsGraphs of polynomialsMidline, amplitude, and period reviewEnd behavior of polynomialsGraph sinusoidal functionsEquation of a hyperbola from featuresEnd behavior of rational functionsAmplitude of sinusoidal functions from equationGraph sinusoidal functions: phase shiftGraphs of rational functionsRational functions: zeros, asymptotes, and undefined pointsVertices & direction of a hyperbolaEvaluate step functionsPeriod of sinusoidal functions from equationEnd behavior of polynomialsPeriodicity of algebraic modelsZeros of polynomials (with factoring)Positive & negative intervals of polynomialsPiecewise functions graphsZeros of polynomials (multiplicity)Solving equations graphically: word problemsEllipse standard equation & graphGraph & features of ellipsesModeling with sinusoidal functions: phase shiftFoci of a hyperbola from equationFoci of an ellipse from radiiAmplitude of sinusoidal functions from graphMidline of sinusoidal functions from equationZeros of polynomials (factored form)Evaluate piecewise functionsPeriod of sinusoidal functions from graphMidline of sinusoidal functions from graphInterpreting trigonometric graphs in contextModeling with sinusoidal functionsGraph 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 ellipsesIntro to hyperbolasGraphing hyperbolas (old example)Equation of a hyperbola not centered at the originFoci of an ellipse from equationFoci of a hyperbola from equationProof of the hyperbola foci formulaGraphing rational functions according to asymptotesTrig word problem: modeling annual temperatureGraphs of rational functions: horizontal asymptoteVertices & direction of a hyperbolaPeriodicity of algebraic modelsPositive and negative intervals of polynomialsFeatures of sinusoidal functionsZeros of polynomials (with factoring): groupingTrig word problem: solving for temperatureMultiplicity of zeros of polynomialsEnd behavior of rational functionsWorked example: graphing piecewise 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 polynomialsWorked example: evaluating piecewise functionsGraph of y=tan(x)Introduction to piecewise functionsStructure in rational expressionZeros of polynomials: plotting zerosWorked example: domain & range of piecewise linear functionsEllipse graph from standard equationIntro to end behavior of polynomialsVertices & direction of a hyperbola (example 2)Interpreting trigonometric graphs in contextGraphs of rational functions: y-interceptDiscontinuities of rational functionsGraphs of rational functions: vertical asymptotesWorked example: domain & range of step functionTrig word problem: modeling daily temperatureZeros of polynomials (with factoring): common factorZeros of polynomials (multiplicity)Zeros of polynomials introductionEllipse standard equation from graph
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