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Funksies van die vorm y = a b ( x ) + q

Funksies van die vorm y = a b ( x ) + q is bekend as eksponensiële funksies. Die algemene vorm van ‘n funksie van hierdie tipe word gewys in [link] .

Algemene vorm en posisie van die grafiek van ‘n funksie met die vorm f ( x ) = a b ( x ) + q .

Ondersoek: funksies van die vorm y = a b ( x ) + q

  1. Op dieselfde assestelsel, skets die volgende grafieke:
    1. a ( x ) = - 2 . b ( x ) + 1
    2. b ( x ) = - 1 . b ( x ) + 1
    3. c ( x ) = - 0 . b ( x ) + 1
    4. d ( x ) = - 1 . b ( x ) + 1
    5. e ( x ) = - 2 . b ( x ) + 1
    Gebruik jou antwoorde om 'n gevolgtrekking ten opsigte van die invloed van a te maak.
  2. Op dieselfde assestelsel, skets die volgende grafieke:
    1. f ( x ) = 1 . b ( x ) - 2
    2. g ( x ) = 1 . b ( x ) - 1
    3. h ( x ) = 1 . b ( x ) + 0
    4. j ( x ) = 1 . b ( x ) + 1
    5. k ( x ) = 1 . b ( x ) + 2
    Gebruik jou antwoorde om 'n gevolgtrekking ten opsigte van die invloed van q te maak.

Jy sou gevind het dat die waarde van a bepaal die vorm van die grafiek, dit wil sê: “Curves Upwards” – “CU” ( a > 0 ) of “Curves Downwards” – “CD” ( a < 0 ).

Jy sou ook gevind het die waarde van q bepaal die posisie van die y -afsnit.

Hierdie verskillende eienskappe word opgesom in [link] .

Getabelleerde opsomming van algemene vorms en posisies van funksies van die vorm y = a b ( x ) + q
a > 0 a < 0
q > 0
q < 0

Definisieversameling en waardeversameling

Vir y = a b ( x ) + q , is die funksie gedefinieer vir alle reële waardes van x . Dus, die definisieversameling is { x : x R } .

Die waardeversameling van y = a b ( x ) + q word bepaal deur die teken van a .

As a > 0 dan:

b ( x ) 0 a · b ( x ) 0 a · b ( x ) + q q f ( x ) q

Dus, as a > 0 , dan is die waardeversameling { f ( x ) : f ( x ) [ q ; ) } .

As a < 0 dan:

b ( x ) 0 a · b ( x ) 0 a · b ( x ) + q q f ( x ) q

Dus, as a < 0 , dan is die waardeversameling { f ( x ) : f ( x ) ( - ; q ] } .

Byvoorbeeld, die definisieversameling van g ( x ) = 3 . 2 x + 2 is { x : x R } . Vir die waardeversameling,

2 x 0 3 · 2 x 0 3 · 2 x + 2 2

Dus is die waardeversameling { g ( x ) : g ( x ) [ 2 ; ) } .

Afsnitte

Vir funksies van die vorm, y = a b ( x ) + q , word die afsnitte met die x en y -as bereken deur x = 0 te stel vir die y -afsnit en deur y = 0 te stel vir die x -afsnit.

Die y -afsnit word as volg bereken:

y = a b ( x ) + q y i n t = a b ( 0 ) + q = a ( 1 ) + q = a + q

Byvoorbeeld, die y -afsnit van g ( x ) = 3 . 2 x + 2 word gegee deur x = 0 te stel, om dan te kry:

y = 3 . 2 x + 2 y i n t = 3 . 2 0 + 2 = 3 + 2 = 5

Die x -afsnitte word bereken deur y = 0 te stel, soos volg:

y = a b ( x ) + q 0 = a b ( x i n t ) + q a b ( x i n t ) = - q b ( x i n t ) = - q a

Dit het net ‘n rëele oplossing as een van beide a < 0 of q < 0 . Anders, het die grafiek van die vorm y = a b ( x ) + q geen x -afsnitte.

Byvoorbeeld, die x -afsnit van g ( x ) = 3 . 2 x + 2 word gegee deur y = 0 te stel:

y = 3 · 2 x + 2 0 = 3 · 2 x i n t + 2 - 2 = 3 · 2 x i n t 2 x i n t = - 2 3

en dit het geen rëele oplossing nie. Dus, die grafiek van g ( x ) = 3 . 2 x + 2 het geen x -afsnitte nie.

Asimptote

Daar is een asimptoot vir funksies van die vorm y = a b ( x ) + q . Die asimptoot kan bepaal word deur die analise van die waardeversameling.

Ons het gesien dat die terrein bepaal word deur die waarde van q. As a > 0 , dan is die terrein { f ( x ) : f ( x ) [ q ; ) } .

Dit wys dat die funksiewaarde neig na die waarde van q as x . Dus die horisontale asimptoot lê by y = q .

Sketse van grafieke van die vorm f ( x ) = a b ( x ) + q

Om grafieke te skets van funksies van die vorm, f ( x ) = a b ( x ) + q , moet ons vier eienskappe bereken:

  1. Definisieversameling en Waardeversameling
  2. y -afsnit
  3. x -afsnit

Byvoorbeeld, skets die grafiek van g ( x ) = 3 . 2 x + 2 . Merk die afsnitte.

Ons het die definisieversameling bepaal om { x : x R } te wees en die waardeversameling om { g ( x ) : g ( x ) ( 2 , ) } te wees.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
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Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
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Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
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Alexandre
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Brian Reply
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
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LITNING Reply
What is meant by 'nano scale'?
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What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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Damian Reply
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Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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Adin Reply
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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