4: Kazi
- Page ID
- 164604
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 4.1: Ufafanuzi wa Kazi
- Kazi ni sheria ambayo inateua kila kipengele katika seti ya maadili ya pembejeo (uwanja), kipengele kimoja na kimoja tu katika seti ya maadili ya pato (upeo).
- 4.2: Uthibitishaji wa Kazi
- Kazi zimeandikwa kama” f (x) = kujieleza algebraic”. Tangu y = f (x), f (x) ni kitu kimoja kama y. nukuu hii inaonyesha x kama pembejeo katika kazi, na f (x) kama pato kutoka kazi.
- 4.3: Kutathmini Kazi
- Wakati kazi ni tathmini, kuchukua nafasi ya x na kupewa thamani numeric au kujieleza algebraic, na kisha kurahisisha matokeo.
- 4.4: Kazi za mstari
- Kazi ya Linear ni kazi ambayo ina fomu f (x) =mx+b. Mstari wowote ambao unaweza kuonyeshwa kwa fomu y=mx+b pia ni kazi.
- 4.5: Kazi kamili ya Thamani
- Ili kuunda kazi za thamani kamili, chagua maadili madogo ya x, na uhesabu thamani ya f (x) kutoka kwa kazi iliyotolewa ili kuunda jozi zilizoamriwa. Tatu zilizoamriwa jozi ni kiasi cha chini kinachohitajika ili graph kazi ya thamani kamili.
- 4.6: Kazi nyingi
- Kazi ya Polynomial ni kazi ambayo inaweza kuandikwa kwa fomu ya jumla.
- 4.7: Domain na Aina ya Kazi
- Domain ya kazi ni maadili yote iwezekanavyo ya x ambayo inaweza kutumika kama pembejeo kwa kazi, ambayo itasababisha idadi halisi kama pato. Aina ya kazi ni seti ya maadili yote ya pato iwezekanavyo ya kazi.
- 4.8: Kazi za kuchora (bila kutumia Calculus)
- Kuna baadhi ya kazi za msingi, aitwaye kazi toolkit, kwamba wanafunzi wanapaswa kutambua kwa ufafanuzi wao kazi na grafu yao. Kwa kila moja ya kazi hizi, x ni variable pembejeo, na f (x) ni variable pato.
- 4.9: Utungaji wa Kazi
- Nukuu f (g (x)) na g (f (x)) inaweza kuwa rahisi kuelewa kuliko kutumia operator wa utungaji. Kwa f (g (x)), fikiria kuifunga mfuko. Zawadi huwekwa ndani ya sanduku (zawadi ni g (x), sanduku ni f (x)) na sasa iliyotiwa, f (x), ina zawadi g (x).
- 4.10: Kupata Mizizi yote ya Real ya Kazi
- Ili kupata mizizi halisi ya kazi, tafuta ambapo kazi inakabiliana na x-axis. Ili kupata ambapo kazi inakabiliana na x-axis, weka f (x) =0 na kutatua equation kwa x.
- 4.11: Kazi ya Ufafanuzi wa Kipande
- Kazi zilizoelezwa kwa kipande ni kazi ambazo hufafanuliwa kwa kutumia milinganyo tofauti kwa sehemu tofauti za kikoa.
- 4.12: Mifano ya Matumizi ya Kazi
- Mifano iliyowekwa ya kazi (matatizo ya neno la AKA!) inaweza kuchukua aina nyingi.


