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9.4: Exercises

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    49006

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    Exercise \(\PageIndex{1}\)

    Which of the graphs below could be the graphs of a polynomial?

    1. clipboard_eccd4976a4db98c81906d1411e9de1c2d.png
    2. clipboard_ed06a093aa7fb90025ab36bbecd8dc67e.png
    3. clipboard_e179b42dfd4f4478f997f38745199e6a0.png
    4. clipboard_ea1dbd3f00355895daf82d6d615a9ffd4.png
    5. clipboard_eaa388b50a4f49148ea8adcf824a57989.png
    6. clipboard_ed6576ca05b12277bf6bfd1d76fce89ba.png
    Answer
    1. yes
    2. no (due to the discontinuity)
    3. no (due to horizontal asymptote)
    4. no (due to corner)
    5. yes (polynomial of degree 1)
    6. yes

    Exercise \(\PageIndex{2}\)

    Identify each of the graphs (a)-(e) with its corresponding assignment from (i)-(vi) below.

    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. \(f(x)=x^4\)
    Answer
    1. corresponds to (iii)
    2. corresponds to (v)
    3. corresponds to (vi)
    4. corresponds to (ii)
    5. corresponds to (iv)

    Exercise \(\PageIndex{3}\)

    Identify the graph with its assignment below.

    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. \(f(x)=x^5-13x^4+65x^3-155x^2+174x-72\)
    Answer
    1. corresponds to (iii)
    2. corresponds to (i)
    3. corresponds to (ii)

    Exercise \(\PageIndex{4}\)

    Sketch the graph of the function with the TI-84, which includes all extrema and intercepts of the graph.

    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. \(f(x)=0.025 x^4+0.0975 x^3-1.215 x^2+2.89 x-22\)
    Answer
    1. clipboard_e601918625705d412d198c78b85bcc8d1.png
    2. clipboard_e634dd9243ea604d148bcf3630b7006f7.png
    3. clipboard_ed3984d1c063d72c0d604473c78edf2fe.png
    4. clipboard_e0218a4e575d060060b3e27a7e48a61c0.png
    5. clipboard_e45559a0b1e714df5d63b26c4da709979.png
    6. clipboard_e4d1e503dff49a2690c18558ec2a32316.png

    Exercise \(\PageIndex{4}\)

    Find the exact value of at least one root of the given polynomial.

    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. \(f(x)=x^4-6x^3+3x^2+5x\)
    Answer
    1. \(x = 2\), \(x = 3\), or \(x = 5\)
    2. \(x = −1\)
    3. \(x = 11\)
    4. \(x = −8\), \(x = −3\), \(x = −2\), or \(x = 4\)
    5. \(x=-3 \pm \sqrt{6}\) (use the quadratic formula)
    6. \(x = 0\)

    Exercise \(\PageIndex{5}\)

    Graph the following polynomials without using the calculator.

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

    This page titled 9.4: Exercises 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; a detailed edit history is available upon request.