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Sec 2.6
Families of Functions
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Parent FunctionParent Function: the simpliest form in a set of functions that form a family.Transformation: different functions in the family.
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Graph y = xGraph the following equations on the graph above.y = x + 2y = x + 4y = x – 2y = x – 4
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Graph y = x2
Graph the following equations on the graph above.y = x2 + 1y = x2 + 2y = x2 – 2y = x2 – 4
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Graph y = x2
Graph the following equations on the graph above.y = (x 1)2y = (x 4)2y = (x + 2)2y = (x + 3)2
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Transformations of f(x)Vertical Translations:Translation up k units, k > 0; y = f(x) + kTranslation down k units, k < 0; y = f(x) – k
Horizontal Translations:Translation right h units, h > 0; y = f(x – h)Translation left h units, h < 0; y = f(x + h)
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Transformations of f(x) cont.Vertical stretches and compressions:Vertical stretch, a > 1; y = af(x)Vertical compression, 0 < a < 1; y = af(x)Reflection:In the xaxis; y = f(x)In the yaxis; y = f(x)
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General Equation
y=a f(x h) + k
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Piecewise FunctionPiecewise function: a function that has different rules for different parts of the domain.
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Graph
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Graph
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Graph
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