math-2a lesson 6-5 - jefflongnuames.weebly.com · lesson 6-5 piece-wise defined function. name:...
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![Page 1: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/1.jpg)
Math-2ALesson 6-5
Piece-wise Defined Function
![Page 2: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/2.jpg)
Name: ____________________ Quiz 6-5 Period: __________
1. What is the equation?
2. What is the domain for the graph below?
3. What is the range for the graph below?
4. What does “inflection point” mean?
5. What two functions have “inflection points”?
6. Which function does not have domain of “all real numbers”?
7. What functions have either an “absolute max”
or an “absolute min” (extrema)?
![Page 3: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/3.jpg)
Set-Builder Notation: a way of writing an equation that also
defines the input values to use.
“French Brackets” set
1)( 2 xxf
),(-for x ,1)( 2 xxf
Inputs
____)(____,for x _____,)( xf rule Inputs
outputs
??? x:f(x) ofDomain
),(- x:Domain
outputs rule
Domain of all square functions are “all real numbers”
(redundant to write it in “set-builder” notation).
![Page 4: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/4.jpg)
)}[0, x,{)( xxk
Domain of k(x) = ? ),0[ x
Graph k(x)
xxk )(Endpoint of k(x) = ? (0, 0)
Write k(x) in “set-builder” notation.
Domain of all square root functions are NOT “all real numbers”
(redundant BUT more useful to write it in “set-builder” notation).
![Page 5: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/5.jpg)
)}[2, x,2{)( xxj
Domain of j(x) = ? ),2[ xGraph j(x)
2)( xxj
Endpoint of j(x) = ? (2, 0)
Write j(x) in “set-builder” notation.
![Page 6: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/6.jpg)
1)( 2 xxk
What is the equation of the graph?
),1[ x
What is the domain of the graph?
)}[-1, x,1{)( 2 xxk
Write the equation of the graph
above in set-builder notation.
![Page 7: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/7.jpg)
p(x)
Define p(x) using “set-builder” notation.
,2](-for x ,1)( 2 xxp
![Page 8: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/8.jpg)
m(x)
Define m(x) using “set-builder” notation.
),1[]5.1,(-for x ,1)( 2 xxm
![Page 9: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/9.jpg)
)}[0,]1,( x,1{)( 2 xxj
Graph j(x)
![Page 10: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/10.jpg)
)}2,(,32{)( xxxf )},2[,)2{()( 2 xxxg
What is the equation
of the graph?
What is the equation
of the graph?
![Page 11: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/11.jpg)
How would you define the following graph?
),2[,)2(
)2 ,(,32)(
2 xx
xxxh
We call this a “piece-wise” defined
![Page 12: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/12.jpg)
Graph them both:
]0,(,14.0
),0(,2)(
2
3
xx
xxxh
![Page 13: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/13.jpg)
But, put them on the same x-y plot:
]0,(,14.0
),0(,2)(
2
3
xx
xxxh
![Page 14: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/14.jpg)
Now erase the part of the graph for each that
does not apply based upon “restricted domain”.
]0,(,1
),0(,2)(
2
3
xx
xxxh
![Page 15: Math-2A Lesson 6-5 - jefflongnuames.weebly.com · Lesson 6-5 Piece-wise Defined Function. Name: _____ Quiz 6-5 Period: _____ 1. What is the equation? 2. What is the domain for the](https://reader034.vdocument.in/reader034/viewer/2022050303/5f6c1f9afafd13223e64185b/html5/thumbnails/15.jpg)
Graph this piecewise-defined function:
),0[,32
)1,(,1)(
xx
xxxg
),0[,
)0,(,)(
2
xx
xxxh
),0[,1
)0,(,)(
3
xx
xxxk