A1:F-BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative). Without technology, find the value of k given the graphs of linear and quadratic functions. With technology, experiment with cases and illustrate an explanation of the effects on the graphs that include cases where f(x) is a linear, quadratic, piecewise linear (to include absolute value), or exponential function.

Khan Academy Resources

Function symmetry introductionSymmetry of polynomialsRadical functions & their graphsGraph sinusoidal functionsEven and odd functions: Graphs and tablesIdentify function transformationsGraphs of logarithmic functionsScale functions horizontallyAmplitude of sinusoidal functions from equationGraph sinusoidal functions: phase shiftScale & reflect absolute value graphsConstruct sinusoidal functionsPeriod of sinusoidal functions from equationGraphs of square and cube root functionsReflect functionsGraphs of exponential functionsShift functionsScale functions verticallyScale & reflect parabolasEven & odd functions: EquationsShift absolute value graphsMidline of sinusoidal functions from equationShift parabolasAmplitude & period of sinusoidal functions from equationTransforming sinusoidal graphs: vertical & horizontal stretchesTransforming sinusoidal graphs: vertical stretch & horizontal reflectionFunction symmetry introductionTransforming exponential graphsEven and odd functions: GraphsShifting absolute value graphsScaling functions introductionScaling & reflecting absolute value functions: graphScaling & reflecting parabolasEven and odd functions: TablesGraphing logarithmic functions (example 1)Scaling functions horizontally: examplesShifting functions introductionIntro to parabola transformationsReflecting functions: examplesTransforming exponential graphs (example 2)Shifting parabolasShifting functions examplesScaling & reflecting absolute value functions: equationGraphing exponential functionsReflecting functions introductionIdentifying function transformationsScaling functions vertically: examplesGraphing shifted functionsEven and odd functions: EquationsEven and odd functions: Find the mistakeSinusoidal function from graphIdentifying horizontal squash from graphGraphing logarithmic functions (example 2)

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