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9.4: Ejercicios

  • Page ID
    117650
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    Ejercicio\(\PageIndex{1}\)

    ¿Cuáles de las siguientes gráficas podrían ser las gráficas de un polinomio?

    1. clipboard_eccd4976a4db98c81906d1411e9de1c2d.png
    2. clipboard_ed06a093aa7fb90025ab36bbecd8dc67e.png
    3. clipboard_e179b42dfd4f4478f997f38745199e6a0.png
    4. clipboard_ea1dbd3f00355895daf82d6d615a9ffd4.png
    5. clipboard_eaa388b50a4f49148ea8adcf824a57989.png
    6. clipboard_ed6576ca05b12277bf6bfd1d76fce89ba.png
    Contestar
    1. si
    2. no (debido a la discontinuidad)
    3. no (debido a la asíntota horizontal)
    4. no (debido a esquina)
    5. sí (polinomio de grado 1)
    6. si

    Ejercicio\(\PageIndex{2}\)

    Identificar cada una de las gráficas (a) - (e) con su correspondiente asignación de (i) - (vi) a continuación.

    1. clipboard_ef52a00bcb5d083a3e9861c73f17f2ef7.png
    2. clipboard_eae5247acf7ce48db71576f139230ecff.png
    3. clipboard_e03c102e59fada6f4816b51f91dc3a527.png
    4. clipboard_e3516c1d5c2a05f6618448181985cbe9a.png
    5. clipboard_efe1203f1e8c7e22f48cc5aee5bd510f8.png
    1. \(f(x)=-x^2\)
    2. \(f(x)=-0.2x^2+1.8\)
    3. \(f(x)=-0.6 x +3.8\)
    4. \(f(x)=-0.2 x^3+0.4x^2+x-0.6\)
    5. \(f(x)=x^3-6x^2+11x-4\)
    6. \(f(x)=x^4\)
    Contestar
    1. corresponde a (iii)
    2. corresponde a (v)
    3. corresponde a (vi)
    4. corresponde a (ii)
    5. corresponde a (iv)

    Ejercicio\(\PageIndex{3}\)

    Identifique la gráfica con su asignación a continuación.

    1. clipboard_e937e195944465f3182f7aae76eb09784.png
    2. clipboard_ee90939bbdd8a45549af47046eceda3e0.png
    3. clipboard_ea63c3680b937f4abd162a7c6f3bb0ab8.png
    1. \(f(x)=x^6-14x^5+78.76 x^4-227.5 x^3+355.25x^2-283.5x+93\)
    2. \(f(x)=-2x^5+30x^4-176x^3+504x^2-704x+386\)
    3. \(f(x)=x^5-13x^4+65x^3-155x^2+174x-72\)
    Contestar
    1. corresponde a (iii)
    2. corresponde a (i)
    3. corresponde a (ii)

    Ejercicio\(\PageIndex{4}\)

    Esboce la gráfica de la función con el TI-84, que incluye todos los extrema e intercepciones de la gráfica.

    1. \(f(x)=0.002 x^3+0.2 x^2-0.05x-5\)
    2. \(f(x)=x^3+4x+50\)
    3. \(f(x)=0.01 x^4-0.101 x^3-3 x^2+50.3x\)
    4. \(f(x)=x^3-.007x\)
    5. \(f(x)=x^3+.007x\)
    6. \(f(x)=0.025 x^4+0.0975 x^3-1.215 x^2+2.89 x-22\)
    Contestar
    1. clipboard_e601918625705d412d198c78b85bcc8d1.png
    2. clipboard_e634dd9243ea604d148bcf3630b7006f7.png
    3. clipboard_ed3984d1c063d72c0d604473c78edf2fe.png
    4. clipboard_e0218a4e575d060060b3e27a7e48a61c0.png
    5. clipboard_e45559a0b1e714df5d63b26c4da709979.png
    6. clipboard_e4d1e503dff49a2690c18558ec2a32316.png

    Ejercicio\(\PageIndex{4}\)

    Encuentra el valor exacto de al menos una raíz del polinomio dado.

    1. \(f(x)=x^3-10x^2+31x-30\)
    2. \(f(x)=-x^3-x^2+8x+8\)
    3. \(f(x)=x^3-11x^2-3x+33\)
    4. \(f(x)=x^4+9x^3-6x^2-136x-192\)
    5. \(f(x)=x^2+6x+3\)
    6. \(f(x)=x^4-6x^3+3x^2+5x\)
    Contestar
    1. \(x = 2\),\(x = 3\), o\(x = 5\)
    2. \(x = −1\)
    3. \(x = 11\)
    4. \(x = −8\),\(x = −3\),\(x = −2\), o\(x = 4\)
    5. \(x=-3 \pm \sqrt{6}\)(utilice la fórmula cuadrática)
    6. \(x = 0\)

    Ejercicio\(\PageIndex{5}\)

    Grafica los siguientes polinomios sin usar la calculadora.

    1. \(f(x)=(x+4)^2(x-5)\)
    2. \(f(x)=-3(x+2)^3 x^2 (x-4)^5\)
    3. \(f(x)=2(x-3)^2(x-5)^3(x-7)\)
    4. \(f(x)=-(x+4)(x+3)(x+2)^2(x+1)(x-2)^2\)
    Contestar
    1. clipboard_ef4f92d6e177498b749141401ce6bcb3c.png
    2. clipboard_ede182b55ff389b4e633a1b348b839e19.png
    3. clipboard_e658546592435a7fe5467a50092a50fbe.png
    4. clipboard_e415fac322053d29c89691f9f54b735e4.png

    This page titled 9.4: Ejercicios is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Thomas Tradler and Holly Carley (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform.