parent functions - mrs. bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11....
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Parent FunctionsDomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Constant
y = kf(x) = k
where k is R
* a horizontal line
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Identity (Linear)
f(x) = x
or
y = x
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Absolute Value
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Power Functions
2 example parents: quadraticcubic
other examples:
Even Powered ParentQuadratic
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHA
Odd Powered Parent
Cubic
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Radical Functions
Even Index Odd Index
Square Root
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Cube Root
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Rational Functions
the ratio of 2 polynomial functionsx≠0
Odd Power in Den.
x≠0
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Even Power in Den.
x≠0
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Exponential
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Logarithmic
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Step-Functions
Greatest Integer - one of several step functions(converts a real number x into the largest integer that is less than or equal to x)
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Logistic
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Sine
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
Cosine
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
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
Characteristics will vary for each piecewise function
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