Calculus

Precalculus: Graphical, Numerical, Algebraic | 8th Edition | ISBN: 9780321656933 | Authors: Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy, Dave Bock
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Author: Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy, Dave Bock
Publisher: Pearson
ISBN: 9780321656933
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Chapter 2 Problems

Chapter: 2 Problem: 2.1.1.177

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, factor the polynomial into linear factors. \(x^{2}-x-12\)

Chapter: 2 Problem: 2.1.1.178

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, factor the polynomial into linear factors. \(x^{2}-11 x+28\)

Chapter: 2 Problem: 2.1.1.179

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, factor the polynomial into linear factors. \(3 x^{2}-11 x+6\)

Chapter: 2 Problem: 2.1.1.180

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, factor the polynomial into linear factors. \(6 x^{2}-5 x+1\)

Chapter: 2 Problem: 2.1.1.181

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, factor the polynomial into linear factors. \(3 x^{3}-5 x^{2}+2 x\)

Chapter: 2 Problem: 2.1.1.182

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, factor the polynomial into linear factors. \(6 x^{3}-22 x^{2}+12 x\)

Chapter: 2 Problem: 2.1.1.183

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, solve the equation mentally. x(x - 1) = 0

Chapter: 2 Problem: 2.1.1.184

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, solve the equation mentally. x(x + 2)(x - 5) = 0

Chapter: 2 Problem: 2.1.1.185

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, solve the equation mentally. \((x+6)^{3}(x+3)(x-1.5)=0\)

Chapter: 2 Problem: 2.1.1.186

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, solve the equation mentally. \((x+6)^{2}(x+4)^{4}(x-5)^{3}=0\)

Chapter: 2 Problem: 2.1.1.187

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, describe how to transform the graph of an appropriate monomial function \(f(x)=x^{n}\) into the graph of the given polynomial function. Sketch the transformed graph by hand and support your answer with a grapher. Compute the location of the y-intercept as a check on the transformed g

Chapter: 2 Problem: 2.1.1.188

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, describe how to transform the graph of an appropriate monomial function \(f(x)=x^{n}\) into the graph of the given polynomial function. Sketch the transformed graph by hand and support your answer with a grapher. Compute the location of the y-intercept as a check on the transformed g

Chapter: 2 Problem: 2.1.1.189

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, describe how to transform the graph of an appropriate monomial function \(f(x)=x^{n}\) into the graph of the given polynomial function. Sketch the transformed graph by hand and support your answer with a grapher. Compute the location of the y-intercept as a check on the transformed g

Chapter: 2 Problem: 2.1.1.190

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, describe how to transform the graph of an appropriate monomial function \(f(x)=x^{n}\) into the graph of the given polynomial function. Sketch the transformed graph by hand and support your answer with a grapher. Compute the location of the y-intercept as a check on the transformed g

Chapter: 2 Problem: 2.1.1.191

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, describe how to transform the graph of an appropriate monomial function \(f(x)=x^{n}\) into the graph of the given polynomial function. Sketch the transformed graph by hand and support your answer with a grapher. Compute the location of the y-intercept as a check on the transformed g

Chapter: 2 Problem: 2.1.1.192

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, describe how to transform the graph of an appropriate monomial function \(f(x)=x^{n}\) into the graph of the given polynomial function. Sketch the transformed graph by hand and support your answer with a grapher. Compute the location of the y-intercept as a check on the transformed g

Chapter: 2 Problem: 2.1.1.193

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7 and 8, graph the polynomial function, locate its extrema and zeros, and explain how it is related to the monomials from which it is built. \(f(x)=-x^{4}+2 x\)

Chapter: 2 Problem: 2.1.1.194

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7 and 8, graph the polynomial function, locate its extrema and zeros, and explain how it is related to the monomials from which it is built. \(g(x)=2 x^{4}-5 x^{2}\)

Chapter: 2 Problem: 2.1.1.195

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, match the polynomial function with its graph. Explain your choice. Do not use a graphing calculator. \(f(x)=7 x^{3}-21 x^{2}-91 x+104\)

Chapter: 2 Problem: 2.1.1.196

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, match the polynomial function with its graph. Explain your choice. Do not use a graphing calculator. \(f(x)=-9 x^{3}+27 x^{2}+54 x-73\)

Chapter: 2 Problem: 2.1.1.197

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, match the polynomial function with its graph. Explain your choice. Do not use a graphing calculator. \(f(x)=x^{5}-8 x^{4}+9 x^{3}+58 x^{2}-164 x+69\)

Chapter: 2 Problem: 2.1.1.198

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, match the polynomial function with its graph. Explain your choice. Do not use a graphing calculator. \(f(x)=-x^{5}+3 x^{4}+16 x^{3}-2 x^{2}-95 x-44\)

Chapter: 2 Problem: 2.1.1.199

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, graph the function pairs in the same series of viewing windows. Zoom out until the two graphs look nearly identical and state your final viewing window. \(f(x)=x^{3}-4 x^{2}-5 x-3 \text { and } g(x)=x^{3}\)

Chapter: 2 Problem: 2.1.1.200

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, graph the function pairs in the same series of viewing windows. Zoom out until the two graphs look nearly identical and state your final viewing window. \(f(x)=x^{3}+2 x^{2}-x+5 \text { and } g(x)=x^{3}\)

Chapter: 2 Problem: 2.1.1.201

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, graph the function pairs in the same series of viewing windows. Zoom out until the two graphs look nearly identical and state your final viewing window. \(f(x)=2 x^{3}+3 x^{2}-6 x-15 \text { and } g(x)=2 x^{3}\)

Chapter: 2 Problem: 2.1.1.202

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, graph the function pairs in the same series of viewing windows. Zoom out until the two graphs look nearly identical and state your final viewing window. \(f(x)=3 x^{3}-12 x+17 \text { and } g(x)=3 x^{3}\)

Chapter: 2 Problem: 2.1.1.203

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1724, graph the function in a viewing window that shows all of its extrema and x-intercepts. Describe the end behavior using limits. \(f(x)=(x-1)(x+2)(x+3)\)

Chapter: 2 Problem: 2.1.1.204

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1724, graph the function in a viewing window that shows all of its extrema and x-intercepts. Describe the end behavior using limits. \(f(x)=(2 x-3)(4-x)(x+1)\)

Chapter: 2 Problem: 2.1.1.205

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1724, graph the function in a viewing window that shows all of its extrema and x-intercepts. Describe the end behavior using limits. \(f(x)=-x^{3}+4 x^{2}+31 x-70\)

Chapter: 2 Problem: 2.1.1.206

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1724, graph the function in a viewing window that shows all of its extrema and x-intercepts. Describe the end behavior using limits. \(f(x)=x^{3}-2 x^{2}-41 x+42\)

Chapter: 2 Problem: 2.1.1.207

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1724, graph the function in a viewing window that shows all of its extrema and x-intercepts. Describe the end behavior using limits. \(f(x)=(x-2)^{2}(x+1)(x-3)\)

Chapter: 2 Problem: 2.1.1.208

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1724, graph the function in a viewing window that shows all of its extrema and x-intercepts. Describe the end behavior using limits. \(f(x)=(2 x+1)(x-4)^{3}\)

Chapter: 2 Problem: 2.1.1.209

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1724, graph the function in a viewing window that shows all of its extrema and x-intercepts. Describe the end behavior using limits. \(f(x)=2 x^{4}-5 x^{3}-17 x^{2}+14 x+41\)

Chapter: 2 Problem: 2.1.1.210

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1724, graph the function in a viewing window that shows all of its extrema and x-intercepts. Describe the end behavior using limits. \(f(x)=-3 x^{4}-5 x^{3}+15 x^{2}-5 x+19\)

Chapter: 2 Problem: 2.1.1.211

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, describe the end behavior of the polynomial function using \(\lim _{x \rightarrow \infty} f(x) \text { and } \lim _{x \rightarrow-\infty} f(x)\). \(f(x)=3 x^{4}-5 x^{2}+3\)

Chapter: 2 Problem: 2.1.1.212

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, describe the end behavior of the polynomial function using \(\lim _{x \rightarrow \infty} f(x) \text { and } \lim _{x \rightarrow-\infty} f(x)\). \(f(x)=-x^3+7 x^2-4 x+3\)

Chapter: 2 Problem: 2.1.1.213

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, describe the end behavior of the polynomial function using \(\lim _{x \rightarrow \infty} f(x) \text { and } \lim _{x \rightarrow-\infty} f(x)\). \(f(x)=7 x^2-x^3+3 x-4\)

Chapter: 2 Problem: 2.1.1.214

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, describe the end behavior of the polynomial function using \(\lim _{x \rightarrow \infty} f(x) \text { and } \lim _{x \rightarrow-\infty} f(x)\). \(f(x)=x^3-x^4+3 x^2-2 x+7\)

Chapter: 2 Problem: 2.1.1.215

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, match the polynomial function with its graph. Approximate all of the real zeros of the function. \(f(x)=20 x^{3}+8 x^{2}-83 x+55\)

Chapter: 2 Problem: 2.1.1.216

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, match the polynomial function with its graph. Approximate all of the real zeros of the function. \(f(x)=35 x^{3}-134 x^{2}+93 x-18\)

Chapter: 2 Problem: 2.1.1.217

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, match the polynomial function with its graph. Approximate all of the real zeros of the function. \(f(x)=44 x^{4}-65 x^{3}+x^{2}+17 x+3\)

Chapter: 2 Problem: 2.1.1.218

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, match the polynomial function with its graph. Approximate all of the real zeros of the function. \(f(x)=4 x^{4}-8 x^{3}-19 x^{2}+23 x-6\)

Chapter: 2 Problem: 2.1.1.219

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3338, find the zeros of the function algebraically. \(f(x)=x^{2}+2 x-8\)

Chapter: 2 Problem: 2.1.1.220

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3338, find the zeros of the function algebraically. \(f(x)=3 x^{2}+4 x-4\)

Chapter: 2 Problem: 2.1.1.221

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3338, find the zeros of the function algebraically. \(f(x)=9 x^{2}-3 x-2\)

Chapter: 2 Problem: 2.1.1.222

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3338, find the zeros of the function algebraically. \(f(x)=x^{3}-25 x\)

Chapter: 2 Problem: 2.1.1.223

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3338, find the zeros of the function algebraically. \(f(x)=3 x^{3}-x^{2}-2 x\)

Chapter: 2 Problem: 2.1.1.224

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3338, find the zeros of the function algebraically. \(f(x)=5 x^{3}-5 x^{2}-10 x\)

Chapter: 2 Problem: 2.1.1.225

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, state the degree and list the zeros of the polynomial function. State the multiplicity of each zero and whether the graph crosses the x-axis at the corresponding x-intercept. Then sketch the graph of the polynomial function by hand. \(f(x)=x(x-3)^{2}\)

Chapter: 2 Problem: 2.1.1.226

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, state the degree and list the zeros of the polynomial function. State the multiplicity of each zero and whether the graph crosses the x-axis at the corresponding x-intercept. Then sketch the graph of the polynomial function by hand. \(f(x)=-x^{3}(x-2)\)

Chapter: 2 Problem: 2.1.1.227

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, state the degree and list the zeros of the polynomial function. State the multiplicity of each zero and whether the graph crosses the x-axis at the corresponding x-intercept. Then sketch the graph of the polynomial function by hand. \(f(x)=(x-1)^{3}(x+2)^{2}\)

Chapter: 2 Problem: 2.1.1.228

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, state the degree and list the zeros of the polynomial function. State the multiplicity of each zero and whether the graph crosses the x-axis at the corresponding x-intercept. Then sketch the graph of the polynomial function by hand. \(f(x)=7(x-3)^{2}(x+5)^{4}\)

Chapter: 2 Problem: 2.1.1.229

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, graph the function in a viewing window that shows all of its x-intercepts and approximate all of its zeros. \(f(x)=2 x^{3}+3 x^{2}-7 x-6\)

Chapter: 2 Problem: 2.1.1.230

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, graph the function in a viewing window that shows all of its x-intercepts and approximate all of its zeros. \(f(x)=-x^{3}+3 x^{2}+7 x-2\)

Chapter: 2 Problem: 2.1.1.231

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, graph the function in a viewing window that shows all of its x-intercepts and approximate all of its zeros. \(f(x)=x^{3}+2 x^{2}-4 x-7\)

Chapter: 2 Problem: 2.1.1.232

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, graph the function in a viewing window that shows all of its x-intercepts and approximate all of its zeros. \(f(x)=-x^{4}-3 x^{3}+7 x^{2}+2 x+8\)

Chapter: 2 Problem: 2.1.1.233

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, graph the function in a viewing window that shows all of its x-intercepts and approximate all of its zeros. \(f(x)=x^{4}+3 x^{3}-9 x^{2}+2 x+3\)

Chapter: 2 Problem: 2.1.1.234

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4348, graph the function in a viewing window that shows all of its x-intercepts and approximate all of its zeros. \(f(x)=2 x^{5}-11 x^{4}+4 x^{3}+47 x^{2}-42 x-8\)

Chapter: 2 Problem: 2.1.1.235

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, find the zeros of the function algebraically or graphically. \(f(x)=x^{3}-36 x\)

Chapter: 2 Problem: 2.1.1.236

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, find the zeros of the function algebraically or graphically. \(f(x)=x^{3}+2 x^{2}-109 x-110\)

Chapter: 2 Problem: 2.1.1.237

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, find the zeros of the function algebraically or graphically. \(f(x)=x^{3}-7 x^{2}-49 x+55\)

Chapter: 2 Problem: 2.1.1.238

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, find the zeros of the function algebraically or graphically. \(f(x)=x^{3}-4 x^{2}-44 x+96\)

Chapter: 2 Problem: 2.1.1.239

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, using only algebra, find a cubic function with the given zeros. Support by graphing your answer. 3, -4, 6

Chapter: 2 Problem: 2.1.1.240

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, using only algebra, find a cubic function with the given zeros. Support by graphing your answer. -2, 3,-5

Chapter: 2 Problem: 2.1.1.241

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, using only algebra, find a cubic function with the given zeros. Support by graphing your answer. \(\sqrt{3},-\sqrt{3}, 4\)

Chapter: 2 Problem: 2.1.1.242

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, using only algebra, find a cubic function with the given zeros. Support by graphing your answer. \(1,1+\sqrt{2}, 1-\sqrt{2}\)

Chapter: 2 Problem: 2.1.1.243

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use cubic regression to fit a curve through the four points given in the table.

Chapter: 2 Problem: 2.1.1.244

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use cubic regression to fit a curve through the four points given in the table.

Chapter: 2 Problem: 2.1.1.245

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use quartic regression to fit a curve through the five points given in the table.

Chapter: 2 Problem: 2.1.1.246

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use quartic regression to fit a curve through the five points given in the table.

Chapter: 2 Problem: 2.1.1.247

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6162, explain why the function has at least one real zero. Writing to Learn \(f(x)=x^{7}+x+100\)

Chapter: 2 Problem: 2.1.1.248

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6162, explain why the function has at least one real zero. Writing to Learn \(f(x)=x^{9}-x+50\)

Chapter: 2 Problem: 2.1.1.249

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Stopping Distance A state highway patrol safety division collected the data on stopping distances in Table 2.14 in the next column. (a) Draw a scatter plot of the data. (b) Find the quadratic regression model. (c) Superimpose the regression curve on the scatter plot. (d) Use the regre

Chapter: 2 Problem: 2.1.1.250

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Analyzing Profit Economists for Smith Brothers, Inc., find the company profit P by using the formula P = R - C, where R is the total revenue generated by the business and C is the total cost of operating the business. (a) Using data from past years, the economists determined that \(R(x)=0.0125 x^

Chapter: 2 Problem: 2.1.1.251

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Circulation of Blood Research conducted at a national health research project shows that the speed at which a blood cell travels in an artery depends on its distance from the center of the artery. The function \(v=1.19-1.87 r^{2}\) models the velocity (in centimeters per second) of a cell that is r c

Chapter: 2 Problem: 2.1.1.252

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Volume of a Box Dixie Packaging Co. has contracted to manufacture a box with no top that is to be made by removing squares of width x from the corners of a 15-in. by 60-in. piece of cardboard. (a) Show that the volume of the box is modeled by V(x) = x(60 - 2x)(15 - 2x). (b) Determine x so tha

Chapter: 2 Problem: 2.1.1.253

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Volume of a Box Squares of width x are removed from a 10-cm by 25-cm piece of cardboard, and the resulting edges are folded up to form a box with no top. Determine all values of x so that the volume of the resulting box is at most \(175\mathrm{\ cm}^3\).

Chapter: 2 Problem: 2.1.1.254

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Volume of a Box The function \(V=2666 x-210 x^{2}+ 4 x^{3}\) represents the volume of a box that has been made by removing squares of width x from each corner of a rectangular sheet of material and then folding up the sides. What values are possible for x?

Chapter: 2 Problem: 2.1.1.255

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The graph of \(f(x)=x^{3}-x^{2}-2\) crosses the x-axis between x = 1 and x = 2. Justify your answer.

Chapter: 2 Problem: 2.1.1.256

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The graph of \(g(x)=(x+a)^{2}\) is obtained by translating the graph of \(f(x)=x^{2}\) to the right, then a must be positive. Justify your answer.

Chapter: 2 Problem: 2.1.1.257

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7174, solve the problem without using a calculator Multiple Choice What is the y-intercept of the graph of \(f(x)=2(x-1)^{3}+5 ?\) (A) 7 (B) 5 (C) 3 (D) 2 (E) 1

Chapter: 2 Problem: 2.1.1.258

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7174, solve the problem without using a calculator Multiple Choice What is the multiplicity of the zero \(x=2 \text { in } f(x)=(x-2)^{2}(x+2)^{3}(x+3)^{7} \text { ? }\) (A) 1 (B) 2 (C) 3 (D) 5 (E) 7

Chapter: 2 Problem: 2.1.1.259

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 73 and 74, which of the specified functions might have the given graph? Multiple Choice (A) f(x)=-x(x+2)(2-x) (?) f(x)=-x(x+2)(x-2) (C) \(f(x)=-x^2(x+2)(x-2)\) (D) \(f(x)=-x(x+2)^2(x-2)\) (E) \(f(x)=-x(x+2)(x-2)^2\)

Chapter: 2 Problem: 2.1.1.260

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 73 and 74, which of the specified functions might have the given graph? Multiple Choice (?) \(f(x)=x(x+2)^2(x-2)\) (?) \(f(x)=x(x+2)^2(2-x)\) (C) \(f(x)=x^2(x+2)(x-2)$\) (D) \(f(x)=x(x+2)(x-2)^2\) (E) \(f(x)=x^2(x+2)(x-2)^2$\)

Chapter: 2 Problem: 2.1.1.261

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 75 and 76, two views of the function are given. Writing to Learn Describe why each view of the function \(f(x)=x^{5}-10 x^{4}+2 x^{3}+64 x^{2}-3 x-55\), by itself, may be considered inadequate.

Chapter: 2 Problem: 2.1.1.262

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 75 and 76, two views of the function are given. Writing to Learn Describe why each view of the function \(f(x)=10 x^{4}+19 x^{3}-121 x^{2}+143 x-51\), by itself, may be considered inadequate.

Chapter: 2 Problem: 2.1.1.263

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7780, the function has hidden behavior when viewed in the window \([-10,10] \text { by }[-10,10]\). Describe what behavior is hidden, and state the dimensions of a viewing window that reveals the hidden behavior. \(f(x)=10 x^3-40 x^2+50 x-20\)

Chapter: 2 Problem: 2.1.1.264

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7780, the function has hidden behavior when viewed in the window \([-10,10] \text { by }[-10,10]\). Describe what behavior is hidden, and state the dimensions of a viewing window that reveals the hidden behavior. \(f(x)=0.5\left(x^3-8 x^2+12.99 x-5.94\right)\)

Chapter: 2 Problem: 2.1.1.265

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7780, the function has hidden behavior when viewed in the window \([-10,10] \text { by }[-10,10]\). Describe what behavior is hidden, and state the dimensions of a viewing window that reveals the hidden behavior. \(f(x)=11 x^3-10 x^2+3 x+5\)

Chapter: 2 Problem: 2.1.1.266

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7780, the function has hidden behavior when viewed in the window \([-10,10] \text { by }[-10,10]\). Describe what behavior is hidden, and state the dimensions of a viewing window that reveals the hidden behavior. \(f(x)=33 x^3-100 x^2+101 x-40\)

Chapter: 2 Problem: 2.1.1.267

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Graph the left side of the equation \(3\left(x^{3}-x\right)=a(x-b)^{3}+c .\) Then explain why there are no real numbers a, b, and c that make the equation true. (Hint: Use your knowledge of \(y=x^{3}\) and transformations.)

Chapter: 2 Problem: 2.1.1.268

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Graph the left side of the equation \(x^{4}+3 x^{3}-2 x-3=a(x-b)^{4}+c .\) Then explain why there are no real numbers a, b, and c that make the equation true.

Chapter: 2 Problem: 2.1.1.269

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Looking Ahead to Calculus The figure shows a graph of both \(f(x)=-x^{3}+2 x^{2}+9 x-11\) and the line L defined by \(y=5(x-2)+7\). (a) Confirm that the point Q(2, 7) is a point of intersection of the two graphs. (b) Zoom in at point Q to develop a visual understanding that \(y=5(x-2)

Chapter: 2 Problem: 2.1.1.270

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Looking Ahead to Calculus Consider the function \(f(x)=x^{n}\) where n is an odd integer. (a) Suppose that a is a positive number. Show that the slope of the line through the points \(P(a, f(a))\) and \(Q(-a, f(-a))\), is \(a^{n-1}\). (b) Let \(x_{0}=a^{1 /(n-1)}\). Find an equation of the li

Chapter: 2 Problem: 2.1.1.271

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Derive an Algebraic Model of a Problem Show that the distance x in the figure is a solution of the equation \(x^{4}-16 x^{3}+500 x^{2}-8000 x+32,000=0\) and find the value of D by following these steps. (a) Use the similar triangles in the diagram and the properties of proportions lea

Chapter: 2 Problem: 2.1.1.272

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Learning Activity Consider functions of the form \(f(x)=x^{3}+b x^{2}+x+1\) where b is a nonzero real number. (a) Discuss as a group how the value of b affects the graph of the function. (b) After completing (a), have each member of the group (individually) predict what the graphs of \(

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