NC.M3.F-IF.7
Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; relative maximums and minimums; symmetries; end behavior; period; and discontinuities.
Example Problems
Evaluate:
Evaluate:
Evaluate:
Khan Academy ResourcesAverage rate of change reviewIntro to rational expressionsAbsolute value graphs reviewGraphs of polynomials: Challenge problemsZeros of polynomials & their graphsGraphs of polynomialsEnd behavior of polynomialsSymmetry of algebraic modelsPositive & negative intervals of polynomialsDomain and range from graphEnd behavior of rational functionsGraphs of rational functionsRational functions: zeros, asymptotes, and undefined pointsRewrite exponential expressionsConstruct sinusoidal functionsIncreasing and decreasing intervalsQuadratic word problems (standard form)Average rate of change word problemsEnd behavior of polynomialsGraphing exponential growth & decayPeriodicity of algebraic modelsInterpret quadratic modelsGraph interpretation word problemsUse ratios in right trianglesGraph absolute value functionsComparing linear functions word problemsInterpret parabolas in contextEnd behavior of algebraic modelsGraphs of exponential growthInterpret a quadratic graphPositive & negative intervals of polynomialsLinear models word problemsFunction domain word problemsPiecewise functions graphsLinear equations word problems: graphsEquivalent forms of exponential expressionsModeling with sinusoidal functions: phase shiftAverage rate of change: graphs & tablesRelate ratios in right trianglesQuadratic word problems (vertex form)Exponential vs. linear growth over timeZeros of polynomials (factored form)Evaluate piecewise functionsQuadratic word problems (factored form)Interpret exponential expressions word problemsConnecting exponential graphs with contextsDetermine the domain of functionsModeling with sinusoidal functionsQuadratic word problem: ballIntro to exponential functionsModeling with linear equations: snowLinear equations word problems: earningsExponential function graphLinear graphs word problemsGraphing rational functions according to asymptotesTrig word problem: modeling annual temperatureExamples finding the domain of functionsTrig word problem: length of day (phase shift)Graphs of rational functions: horizontal asymptoteComparing linear functions word problem: workGraphing exponential growth & decayGraphing absolute value functionsPeriodicity of algebraic modelsInterpret quadratic models: Factored formWorked example: determining domain word problem (real numbers)Introduction to average rate of changeEnd behavior of rational functionsWorked example: average rate of change from graphGraphs of exponential growthEnd behavior of algebraic modelsWorked example: graphing piecewise functionsSymmetry of algebraic modelsComparing linear functions word problem: climbQuadratic word problems (vertex form)Graphs of rational functions: zerosSine & cosine of complementary anglesWorked example: average rate of change from tableLinear equations word problems: volcanoWorked example: evaluating piecewise functionsAnalyzing tables of exponential functionsDetermining whether values are in domain of functionAverage rate of change word problem: graphComparing maximum points of quadratic functionsIntroduction to piecewise functionsLinear graphs word problem: catsQuadratic word problems (factored form)Worked examples: Forms & features of quadratic functionsGraph interpretation word problem: temperatureComparing features of quadratic functionsWorked example: domain & range of piecewise linear functionsInterpret quadratic models: Vertex formRewriting exponential expressions as A⋅BᵗIntro to end behavior of polynomialsGraphs of rational functions: y-interceptDiscontinuities of rational functionsEquivalent forms of exponential expressionsGraphs of rational functions: vertical asymptotesWorked example: domain & range of step functionTrig word problem: modeling daily temperatureAnalyzing graphs of exponential functionsComparing linear functions word problem: walkSinusoidal function from graphAnalyzing graphs of exponential functions: negative initial valueUsing complementary anglesGraph interpretation word problem: basketballTrig word problem: complementary anglesAverage rate of change word problem: tableInterpret a quadratic graph

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