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Page 1: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

1

September 19, 2013

Parent FunctionsDomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Constant

  y = kf(x) = k 

where k is R

* a horizontal line

Page 2: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

2

September 19, 2013

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Identity (Linear)

f(x) = x

    or

y = x

Page 3: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

3

September 19, 2013

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Absolute Value

Page 4: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

4

September 19, 2013

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Power Functions

2 example parents: quadraticcubic

other examples:

Page 5: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

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September 19, 2013

Even Powered ParentQuadratic

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHA

Page 6: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

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September 19, 2013

Odd Powered Parent

Cubic

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Page 7: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

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September 19, 2013

Radical Functions

Even Index Odd Index

Square Root

Page 8: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

8

September 19, 2013

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Cube Root

Page 9: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

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September 19, 2013

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Rational Functions

the ratio of 2 polynomial functionsx≠0

Page 10: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

10

September 19, 2013

Odd Power in Den.

x≠0

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Page 11: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

11

September 19, 2013

Even Power in Den.

x≠0

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Page 12: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

12

September 19, 2013

Exponential

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Page 13: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

13

September 19, 2013

Logarithmic

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Page 14: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

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September 19, 2013

Sine

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

Page 15: Parent Functions - misscracroftmath.weebly.com · Parent Functions Domain Range Continuous Increasing Decreasing Constant Left End Right End Symmetry xintercepts yintercepts VA HA

1.3 Lecture.notebook

15

September 19, 2013

Cosine

DomainRangeContinuousIncreasingDecreasingConstantLeft EndRight EndSymmetryx­interceptsy­interceptsVAHABoundedExtrema

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1.3 Lecture.notebook

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September 19, 2013

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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1.3 Lecture.notebook

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September 19, 2013

Characteristics will vary for each piecewise function


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