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3.1E: Kazi na Uthibitishaji wa Kazi (Mazoezi)

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    Kwa mazoezi yafuatayo, onyesha kama uhusiano ni kazi.

    1. \(\{(a, b),(c, d),(e, d)\}\)
    2.\ {(5,2), (6,1), (6,2), (4,8)\}\)
    3. \(y^{2}+4=x,\)kwa\(x\) variable huru na\(y\) variable tegemezi
    4. Je, grafu katika Kielelezo 1 kazi?

    Grafu ya parabola.

    Kwa mazoezi yafuatayo, tathmini kazi katika maadili yaliyoonyeshwa:

    \[\begin{array}{lllll} f(-3) ; & f(2) ; & f(-a) ; & -f(a) ; & f(a+h) .\end{array} \nonumber\]

    5. \(f(x)=-2 x^{2}+3 x\)
    6. \(f(x)=2|3 x-1|\)

    Kwa mazoezi yafuatayo, onyesha kama kazi ni moja kwa moja.

    7. \(f(x)=-3 x+5\)
    8. \(f(x)=\mid x-3\)

    Kwa mazoezi yafuatayo, tumia mtihani wa mstari wa wima ili uone kama uhusiano ambao grafu hutolewa ni kazi.

    9.

    Grafu ya kazi ya ujazo.

    10.

    Grafu ya uhusiano.

    11.

    Grafu ya uhusiano.

    Kwa mazoezi yafuatayo, graph kazi.

    12. \(f(x)=\mid x+1\)
    13. \(f(x)=x^{2}-2\)

    Kwa mazoezi yafuatayo, tumia Kielelezo 2 ili takriban maadili.

    Grafu ya parabola.

    14. \(f(2)\)
    15. \(f(-2)\)
    16. Ikiwa\(f(x)=-2,\) basi tatua\(x\).
    17. Ikiwa\(f(x)=1,\) basi tatua\(x\).

    Kwa mazoezi yafuatayo, tumia kazi\(h(t)=-16 t^{2}+80 t\) ili kupata maadili kwa fomu rahisi.

    18. \(\frac{h(2)-h(1)}{2-1}\)
    19. \(\frac{h(a)-h(1)}{a-1}\)