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Parent FunctionsDomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
Constant
y = kf(x) = k
where k is R
* a horizontal line
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
Identity (Linear)
f(x) = x
or
y = x
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
Absolute Value
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
Power Functions
2 example parents: quadraticcubic
other examples:
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Even Powered ParentQuadratic
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHA
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Odd Powered Parent
Cubic
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
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Radical Functions
Even Index Odd Index
Square Root
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
Cube Root
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
Rational Functions
the ratio of 2 polynomial functionsx≠0
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Odd Power in Den.
x≠0
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
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Even Power in Den.
x≠0
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
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Exponential
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
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Logarithmic
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
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Sine
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
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Cosine
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryxinterceptsyinterceptsVAHABoundedExtrema
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Piecewise Functions
frequently: intervals (parts) of the domain are associated with different functions (related to continuity)
certain pieces of the function have specific behavior
Characteristics will vary for each piecewise function
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Characteristics will vary for each piecewise function