Mienzaniso yeMibvunzo neKukurukurirana kweMabasa eAlgebraic
Mabasa eAlgebraic inyaya inokosha mumasvomhu, inowanzoonekwa mubvunzo dzechikoro nemakwikwi emasvomhu. Kunzwisisa pfungwa yemabasa eAlgebraic uye maitiro ekugadzirisa matambudziko ane chekuita nemusoro uyu ndicho chinhu chikuru kuti unzwisise musoro uyu. Chinyorwa chino chichatsanangura mienzaniso yakati wandei yematambudziko uye chichakurukura mabasa eAlgebraic zvakadzama.
Pendauluan
Basa ihukama hunobatanidza chinhu chimwe nechimwe museti imwe (inonzi domain) nechinhu chimwe chete mune imwe seti (inonzi codomain). Pamasvomhu, basa rinogona kuratidzwa se \( f : A \kusvika B \), apo \( f \) ibasa rinounganidza zvinhu museti \( A \) nezvinhu museti \( B \). Ruzivo rwakajairika rwebasa ndi \( f(x) \), zvinoreva kuti \( f \) ibasa rinoenderana nevariable \( x \).
Muenzaniso Mubvunzo 1: Basa remutsetse
Mubvunzo: Sarudza equation yemutsetse \( f(x) \) unopfuura nepakati pepoindi (2, 3) uye une gradient ye4.
Kukurukurirana:
Basa remutsetse mukuru rine chimiro \( f(x) = mx + c \), apo \( m \) iri gradient uye \( c \) iri y-intercept.
1. Isa kukosha kwegradient \( m = 4 \) mu equation:
\[
f(x) = 4x + c
\]
2. Shandisa poindi (2, 3) kuti uwane \( c \):
\[
3 = 4(2) + c
\]
\[
3 = 8 + c
\]
\[
c = 3 – 8
\]
\[
c = -5
\]
3. Ne \( m = 4 \) uye \( c = -5 \), equation yemutsetse ndeiyi:
\[
f(x) = 4x – 5
\]
Muenzaniso Mubvunzo 2: Mabasa eQuadratic
Mubvunzo: Kana girafu yebasa ikapfuura nemapoinzi (1, 4), (2, 7), uye (3, 12), sarudza kukosha kwe \( a \), \( b \), uye \( c \).
Kukurukurirana:
1. Isa poindi (1, 4) muequation:
\[
4 = a(1)^2 + b(1) + c
\]
\[
4 = a + b + c \quad \text{(Equation 1)}
\]
2. Isa poindi (2, 7) muequation:
\[
7 = a(2)^2 + b(2) + c
\]
\[
7 = 4a + 2b + c \quad \text{(Equation 2)}
\]
3. Isa poindi (3, 12) muequation:
\[
12 = a(3)^2 + b(3) + c
\]
\[
12 = 9a + 3b + c \quad \text{(Equation 3)}
\]
4. Gadzirisa hurongwa hwema equation akatsetseka:
– Bvisa Equation 1 kubva muEquation 2:
\[
(7 – 4) = (4a + 2b + c) – (a + b + c)
\]
\[
3 = 3a + b \quad \text{(Equation 4)}
\]
– Bvisa Equation 2 kubva muEquation 3:
\[
(12 – 7) = (9a + 3b + c) – (4a + 2b + c)
\]
\[
5 = 5a + b \quad \text{(Equation 5)}
\]
5. Bvisa Equation 4 kubva muEquation 5:
\[
(5 – 3) = (5a + b) – (3a + b)
\]
\[
2 = 2a
\]
\[
kuti = 1
\]
6. Isa \( a = 1 \) muEquation 4:
\[
3 = 3(1) + b
\]
\[
3 = 3 + b
\]
\[
b = 0
\]
7. Isa \( a = 1 \) uye \( b = 0 \) muEquation 1:
\[
4 = 1 + 0 + c
\]
\[
c = 3
\]
Saka, kukosha kwe \( a \), \( b \), uye \( c \) ndekwekuti:
\[
a = 1, \quad b = 0, \quad c = 3
\]
Saka, basa re quadratic nderekuti:
\[
f(x) = x^2 + 3
\]
Muenzaniso Mubvunzo 3: Mabasa neTrigonometry
Dambudziko: Kupiwa basa \( f(x) = 2 \sin (x) + \cos (x) \). Sarudza \( f\left(\frac{\pi}{2}\right) \).
Kukurukurirana:
1. Isa \( x = \frac{\pi}{2} \) mu "function":
\[
f\left(\frac{\pi}{2}\right) = 2 \sin \left(\frac{\pi}{2}\right) + \cos \left(\frac{\pi}{2}\right)
\]
2. Yeuka kuti kukosha kwetrigonometric:
\[
\sin\left(\frac{\pi}{2}\right) = 1 \quad \text{and} \quad \cos\left(\frac{\pi}{2}\right) = 0
\]
3. Zvadaro tinowana:
\[
f\left(\frac{\pi}{2}\right) = 2(1) + 0
\]
\[
f\left(\frac{\pi}{2}\right) = 2
\]
Muenzaniso Mubvunzo 4: Kuumbwa kweMabasa
Dambudziko: Zvichienderana nemabasa \( f(x) = 2x + 1 \) uye \( g(x) = x^2 – 3 \). Sarudza \( (f \circ g)(x) \) uye \( (g \circ f)(x) \).
Kukurukurirana:
1. \( (f \circ g)(x) \) :
\[
(f \denderedzwa g)(x) = f(g(x))
\]
Isa \( g(x) \) mu \( f(x) \):
\[
g(x) = x^2 – 3
\]
\[
f(g(x)) = f(x^2 – 3)
\]
Shandisa \( f(x) = 2x + 1 \):
\[
f(x^2 – 3) = 2(x^2 – 3) + 1
\]
\[
= 2x^2 – 6 + 1
\]
\[
= 2x^2 – 5
\]
2. \( (g \circ f)(x) \) :
\[
(g \denderedzwa f)(x) = g(f(x))
\]
Isa \( f(x) \) mu \( g(x) \):
\[
f(x) = 2x + 1
\]
\[
g(f(x)) = g(2x + 1)
\]
Isa \( g(x) = x^2 – 3 \):
\[
g(2x + 1) = (2x + 1)^2 – 3
\]
\[
= 4x^2 + 4x + 1 – 3
\]
\[
= 4x^2 + 4x – 2
\]
Saka, mhedzisiro yekupedzisira:
\[
(f \circ g)(x) = 2x^2 – 5
\]
\[
(g \denderedzwa f)(x) = 4x^2 + 4x – 2
\]
Mhedziso
Mabasa eAlgebraic anosanganisira zvinhu zvakawanda, kubva kumabasa emutsara kusvika kumabasa equadratic kusvika kumabasa ekuumbwa. Chinyorwa chino chinopa mienzaniso yakati wandei yezvinetso pamwe nehurukuro dzakadzama. Kunzwisisa magadzirisirwo ematambudziko aya kuchabatsira zvikuru mukunzwisisa musoro wemabasa ealgebraic uye kushandiswa kwemamwe mazano emasvomhu.
Nekudzidzira nguva dzose uye kunzwisisa kwakasimba kwepfungwa, kugadzirisa matambudziko ebasa realgebra kuchava hunyanzvi hwakavimbika. Ramba uchidzidzira uye usazeza kutsvaga mamwe maturusi ekuwedzera kunzwisisa kwako.
