PC.FBF.3
Describe the effect of the transformations kf(x), f(x)+k, f(x+k), and combinations of such transformations on the graph of y=f(x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph.
Example Problems
A piston's vertical position (in cm) is , where t is seconds.
What is the position at s?
What is the position at s?
An EEG α‑wave signal is µV, where t is in seconds. What is the phase shift expressed in milliseconds?
The magnitude of a variable star is , with in days.
What is its magnitude at days?
What is its magnitude at days?
Khan Academy ResourcesFunction 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 shiftConstruct sinusoidal functionsPeriod of sinusoidal functions from equationGraphs of square and cube root functionsReflect functionsGraphs of exponential functionsShift functionsScale functions verticallyEven & odd functions: EquationsMidline of sinusoidal functions from equationAmplitude & period of sinusoidal functions from equationTransforming sinusoidal graphs: vertical & horizontal stretchesTransforming sinusoidal graphs: vertical stretch & horizontal reflectionFunction symmetry introductionTransforming exponential graphsEven and odd functions: GraphsScaling functions introductionEven and odd functions: TablesGraphing logarithmic functions (example 1)Scaling functions horizontally: examplesShifting functions introductionReflecting functions: examplesTransforming exponential graphs (example 2)Shifting functions examplesGraphing 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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