9.4: Exercises
- Page ID
- 49006
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Which of the graphs below could be the graphs of a polynomial?
- Answer
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- yes
- no (due to the discontinuity)
- no (due to horizontal asymptote)
- no (due to corner)
- yes (polynomial of degree 1)
- yes
Identify each of the graphs (a)-(e) with its corresponding assignment from (i)-(vi) below.
- \(f(x)=-x^2\)
- \(f(x)=-0.2x^2+1.8\)
- \(f(x)=-0.6 x +3.8\)
- \(f(x)=-0.2 x^3+0.4x^2+x-0.6\)
- \(f(x)=x^3-6x^2+11x-4\)
- \(f(x)=x^4\)
- Answer
-
- corresponds to (iii)
- corresponds to (v)
- corresponds to (vi)
- corresponds to (ii)
- corresponds to (iv)
Identify the graph with its assignment below.
- \(f(x)=x^6-14x^5+78.76 x^4-227.5 x^3+355.25x^2-283.5x+93\)
- \(f(x)=-2x^5+30x^4-176x^3+504x^2-704x+386\)
- \(f(x)=x^5-13x^4+65x^3-155x^2+174x-72\)
- Answer
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- corresponds to (iii)
- corresponds to (i)
- corresponds to (ii)
Sketch the graph of the function with the TI-84, which includes all extrema and intercepts of the graph.
- \(f(x)=0.002 x^3+0.2 x^2-0.05x-5\)
- \(f(x)=x^3+4x+50\)
- \(f(x)=0.01 x^4-0.101 x^3-3 x^2+50.3x\)
- \(f(x)=x^3-.007x\)
- \(f(x)=x^3+.007x\)
- \(f(x)=0.025 x^4+0.0975 x^3-1.215 x^2+2.89 x-22\)
- Answer
-
Find the exact value of at least one root of the given polynomial.
- \(f(x)=x^3-10x^2+31x-30\)
- \(f(x)=-x^3-x^2+8x+8\)
- \(f(x)=x^3-11x^2-3x+33\)
- \(f(x)=x^4+9x^3-6x^2-136x-192\)
- \(f(x)=x^2+6x+3\)
- \(f(x)=x^4-6x^3+3x^2+5x\)
- Answer
-
- \(x = 2\), \(x = 3\), or \(x = 5\)
- \(x = −1\)
- \(x = 11\)
- \(x = −8\), \(x = −3\), \(x = −2\), or \(x = 4\)
- \(x=-3 \pm \sqrt{6}\) (use the quadratic formula)
- \(x = 0\)
Graph the following polynomials without using the calculator.
- \(f(x)=(x+4)^2(x-5)\)
- \(f(x)=-3(x+2)^3 x^2 (x-4)^5\)
- \(f(x)=2(x-3)^2(x-5)^3(x-7)\)
- \(f(x)=-(x+4)(x+3)(x+2)^2(x+1)(x-2)^2\)
- Answer
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