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4.4: Kazi za mstari

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    164673

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    Ufafanuzi: Kazi ya mstari

    Kazi ya Linear ni kazi ambayo ina fomu\(f(x) = mx+b\). Mstari wowote ambao unaweza kuonyeshwa kwa fomu pia\(y = mx + b\) ni kazi.

    Matumizi kazi nukuu wakati equation ya mstari imeandikwa katika aina Slope-Intercept haina mapungufu au mapumziko na mstari si mstari wima. Kazi ya mstari imeandikwa kama\(f(x) = mx + b\) kupitisha mtihani wa mstari wa wima:

    Ufafanuzi: Mtihani wa Mstari

    Mtihani wa Mstari wa Wima hutumiwa kuamua kama grafu inafafanua pato la wima kama kazi ya pembejeo ya usawa. Ikiwa mstari wowote wa wima utavuka grafu zaidi ya mara moja, basi grafu haina kufafanua pato moja tu la wima kwa kila pembejeo ya usawa.

    Kwa habari zaidi kuhusu equations linear, rejea sehemu ya mistari moja kwa moja.

    Mfano Template:index

    Unda meza ya ufumbuzi na grafu kazi zifuatazo za mstari:

    \(f(x) = 2x − 3\)

    Suluhisho

    \(f(x) = 2x − 3\)

    Ili kupata jozi mbili zilizoamuru, kuchagua maadili madogo ya\(x\), kisha compute maadili ya\(f(x)\).

    clipboard_e29fd85b9c181a1598af5c64e8ac834a9.png
    Kielelezo Template:index
    Jedwali la Solutions kwa\(f(x) = 2x − 3\)
    \(x\) \(f(x)\)
    -1 \(f(−1) = 2(−1) − 3 = −2 − 3 = −5\)
    0 \(f(0) = 2(0) − 3 = 0 − 3 = 3\)
    Mfano Template:index

    Unda meza ya ufumbuzi na grafu kazi inayofuata ya mstari:

    \(g(x) = \dfrac{1}{ 3} x + 4\)

    Suluhisho

    Ili kupata jozi mbili zilizoamuru, chagua maadili madogo ya x, kisha compute maadili ya\(g(x)\). Kwa sababu mgawo wa neno zenye x ni sehemu, chagua wingi wa denominator kwa bidhaa ya\(\dfrac{1 }{3} x\) kuwa integer.

    clipboard_ee79443c652fdf8b732b23ff5aa9bfefd.png
    Kielelezo Template:index
    Jedwali la Solutions kwa\(g(x) =\dfrac{ 1 }{3} x + 4\)
    \(x\) \(g(x)\)
    0 \(g(0) = \dfrac{1 }{3} (0) + 4 = 4\)
    3 \(g(3) = \dfrac{1 }{3} (3) + 4 = 1 + 4 = 5\)
    Mfano Template:index

    Unda meza ya ufumbuzi na grafu kazi zifuatazo za mstari:

    \(h(x) = −4x − 1\)

    Suluhisho

    Ili kupata jozi mbili zilizoamuru, kuchagua maadili madogo ya\(x\), kisha compute maadili ya\(h(x)\).

    clipboard_e9c1e072a5ba446060a941d3080d49668.png
    Kielelezo Template:index
    Jedwali la Solutions kwa\(h(x) = −4x − 1\)
    \(x\) \(h(x)\)
    0 \(h(0) = −4(0) − 1 = −1\)
    1 \(h(1) = −4(1) − 1 = −5\)
    Mfano Template:index

    Unda meza ya ufumbuzi na grafu kazi zifuatazo za mstari:

    \(h(x) = − \dfrac{3 }{4} x − \dfrac{1 }{4}\)

    Suluhisho

    Ili kupata jozi mbili zilizoamriwa\(x\), chagua maadili madogo ya, kisha compute maadili\(h(x)\) ya.Kwa sababu mgawo wa neno zenye\(x\) ni sehemu, chagua wingi wa denominator kwa bidhaa ya\(− \dfrac{3}{4} x\) kuwa integer.

    clipboard_eda0a4847b8349cd771ea227d008b6388.png
    Kielelezo Template:index
    Jedwali la Solutions kwa\(h(x) = − \dfrac{3}{4} x − \dfrac{1}{4}\)
    \(x\) \(h(x)\)
    0 \(h(0) = − \dfrac{3}{4} (0) − \dfrac{1}{4} = − \dfrac{1}{4}\)
    4 \(h(4) = − \dfrac{3}{4} (4) − \dfrac{1}{4} = −3 − \dfrac{1}{4} = −3 \dfrac{1}{4}\)
    Zoezi Template:index

    Unda meza ya ufumbuzi na grafu kazi zifuatazo za mstari:

    1. \(f(x) = 4x − 9\)
    2. \(g(x) = \dfrac{1}{ 2} x − 2\)
    3. \(h(x) = −3x + 5\)
    4. \(f(x) = − \dfrac{2}{ 3} x −\dfrac{ 1 }{3}\)