A2.F-IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend from linear, quadratic and exponential functions to include square root, cube root, polynomial, exponential, logarithmic, sine, cosine, tangent and piecewise-defined functions.

Example Problems
We are given that .
Find an expression for
in terms of x and y.
We are given that .
Find an expression for
in terms of x and y.
We are given that .
Find an expression for
in terms of x and y.
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 polynomialsGraphing exponential growth & decayGraphs of exponential growthPositive & 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 reflectionIntro to exponential functionsExponential function graphTransforming exponential graphsGraphing exponential growth & decayFeatures of sinusoidal functionsGraphs of exponential growthWorked example: graphing piecewise functionsGraphing logarithmic functions (example 1)Example: Graphing y=3⋅sin(½⋅x)-2Example: Graphing y=-cos(π⋅x)+1.5Transforming 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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