A2.13

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales and use them to make predictions. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Khan Academy Resources

Graphs of polynomials: Challenge problemsZeros of polynomials & their graphsGraphs of polynomialsMidline, amplitude, and period reviewEnd behavior of polynomialsRadical functions & their graphsPositive & negative intervals of polynomialsGraph sinusoidal functionsGraphs of logarithmic functionsAmplitude of sinusoidal functions from equationGraph sinusoidal functions: phase shiftIncreasing and decreasing intervalsPeriod of sinusoidal functions from equationGraphs of square and cube root functionsGraphs of exponential functionsEnd behavior of polynomialsPositive & negative intervals of polynomialsPiecewise functions graphsAmplitude 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 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 reflectionTransforming exponential graphsFeatures of sinusoidal functionsWorked example: graphing piecewise functionsGraphing logarithmic functions (example 1)Example: Graphing y=3⋅sin(½⋅x)-2Example: Graphing y=-cos(π⋅x)+1.5Two-variable linear equations introTransforming exponential graphs (example 2)Worked example: evaluating piecewise functionsGraph of y=tan(x)Introduction to piecewise functionsGraphing square and cube root functionsGraphing exponential functionsWorked example: domain & range of piecewise linear functionsIntro to end behavior of polynomialsWorked example: domain & range of step functionGraphical relationship between 2ˣ and log₂(x)Graphing logarithmic functions (example 2)

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