parent functions - mrs. bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11....
TRANSCRIPT
![Page 1: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/1.jpg)
Parent FunctionsDomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 2: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/2.jpg)
Constant
y = kf(x) = k
where k is R
* a horizontal line
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 4: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/4.jpg)
Identity (Linear)
f(x) = x
or
y = x
![Page 5: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/5.jpg)
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 6: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/6.jpg)
Absolute Value
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 8: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/8.jpg)
Power Functions
2 example parents: quadraticcubic
other examples:
![Page 9: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/9.jpg)
Even Powered ParentQuadratic
![Page 10: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/10.jpg)
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHA
![Page 11: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/11.jpg)
Odd Powered Parent
Cubic
![Page 12: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/12.jpg)
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 13: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/13.jpg)
Radical Functions
Even Index Odd Index
![Page 14: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/14.jpg)
Square Root
![Page 15: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/15.jpg)
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 16: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/16.jpg)
Cube Root
![Page 17: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/17.jpg)
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 18: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/18.jpg)
Rational Functions
the ratio of 2 polynomial functionsx≠0
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Odd Power in Den.
x≠0
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 21: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/21.jpg)
Even Power in Den.
x≠0
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 23: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/23.jpg)
Exponential
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 25: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/25.jpg)
Logarithmic
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 27: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/27.jpg)
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)
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 29: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/29.jpg)
Logistic
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 31: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/31.jpg)
Sine
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DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 33: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/33.jpg)
Cosine
![Page 34: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/34.jpg)
DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx-interceptsy-interceptsVAHABoundedExtrema
![Page 35: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/35.jpg)
Piecewise Functions
frequently: intervals (parts) of the domain are associated with different functions (related to continuity)
certain pieces of the function have specific behavior
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Characteristics will vary for each piecewise function
![Page 37: Parent Functions - Mrs. Bramallmrsbramall.weebly.com/uploads/7/8/7/6/7876989/1.3... · 2019. 11. 9. · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left](https://reader033.vdocuments.mx/reader033/viewer/2022060820/60991f3c2d76b85a36068c1e/html5/thumbnails/37.jpg)
Characteristics will vary for each piecewise function