 3.2.1: In Exercises 110, determine which functions are polynomial functio...
 3.2.2: In Exercises 110, determine which functions are polynomial functio...
 3.2.3: In Exercises 110, determine which functions are polynomial functio...
 3.2.4: In Exercises 110, determine which functions are polynomial functio...
 3.2.5: In Exercises 110, determine which functions are polynomial functio...
 3.2.6: In Exercises 110, determine which functions are polynomial functio...
 3.2.7: In Exercises 110, determine which functions are polynomial functio...
 3.2.8: In Exercises 110, determine which functions are polynomial functio...
 3.2.9: In Exercises 110, determine which functions are polynomial functio...
 3.2.10: In Exercises 110, determine which functions are polynomial functio...
 3.2.11: In Exercises 1114, identify which graphs are not those of polynomi...
 3.2.12: In Exercises 1114, identify which graphs are not those of polynomi...
 3.2.13: In Exercises 1114, identify which graphs are not those of polynomi...
 3.2.14: In Exercises 1114, identify which graphs are not those of polynomi...
 3.2.15: In Exercises 1518, use the Leading Coefficient Test to detenuine t...
 3.2.16: In Exercises 15/8, use the Leading Coefficient Test to detenuine t...
 3.2.17: In Exercises 15/8, use the Leading Coefficient Test to detenuine t...
 3.2.18: In Exercises 1518, use the Leading Coefficient Test to detenuine t...
 3.2.19: In Exercises 1924, use the Leading Coefficient Test to detennine t...
 3.2.20: In Exercises 1924, use the Leading Coefficient Test to detennine t...
 3.2.21: In Exercises 1924, use the Leading Coefficient Test to detennine t...
 3.2.22: In Exercises 1924, use the Leading Coefficient Test to detennine t...
 3.2.23: In Exercises 1924, use the Leading Coefficient Test to detennine t...
 3.2.24: In Exercises 1924, use the Leading Coefficient Test to detennine t...
 3.2.25: In Exercises 2532,find the zeros for each polynomial function and ...
 3.2.26: In Exercises 2532,find the zeros for each polynomial function and ...
 3.2.27: In Exercises 2532,find the zeros for each polynomial function and ...
 3.2.28: In Exercises 2532,find the zeros for each polynomial function and ...
 3.2.29: In Exercises 2532,find the zeros for each polynomial function and ...
 3.2.30: In Exercises 2532,find the zeros for each polynomial function and ...
 3.2.31: In Exercises 2532,find the zeros for each polynomial function and ...
 3.2.32: In Exercises 2532,find the zeros for each polynomial function and ...
 3.2.33: In Exercises 3340. usethe Intermediate Value Theorem to show that...
 3.2.34: In Exercises 3340. usethe Intermediate Value Theorem to show that...
 3.2.35: In Exercises 3340. usethe Intermediate Value Theorem to show that...
 3.2.36: In Exercises 3340. usethe Intermediate Value Theorem to show that...
 3.2.37: In Exercises 3340. usethe Intermediate Value Theorem to show that...
 3.2.38: In Exercises 3340. usethe Intermediate Value Theorem to show that...
 3.2.39: In Exercises 3340. usethe Intermediate Value Theorem to show that...
 3.2.40: In Exercises 3340. usethe Intermediate Value Theorem to show that...
 3.2.41: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.42: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.43: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.44: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.45: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.46: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.47: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.48: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.49: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.50: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.51: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.52: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.53: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.54: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.55: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.56: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.57: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.58: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.59: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.60: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.61: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.62: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.63: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.64: In Exercises 4164, a. Use the Leading Coefficient Test to determin...
 3.2.65: In Exercises 6572. complete graphs of polynomial functions whose ...
 3.2.66: In Exercises 6572. complete graphs of polynomial functions whose ...
 3.2.67: In Exercises 6572. complete graphs of polynomial functions whose ...
 3.2.68: In Exercises 6572. complete graphs of polynomial functions whose ...
 3.2.69: In Exercises 6572. complete graphs of polynomial functions whose ...
 3.2.70: In Exercises 6572. complete graphs of polynomial functions whose ...
 3.2.71: In Exercises 6572. complete graphs of polynomial functions whose ...
 3.2.72: In Exercises 6572. complete graphs of polynomial functions whose ...
 3.2.73: Experts fear that withoui conservation effons, tigers could disappe...
 3.2.74: rpens fear that withoui conservation effons, tigers could disappea...
 3.2.75: During a diagnostic evaluation, a 33yearofd woman experienced a p...
 3.2.76: Volatility at the Pump The graph sho"' the average price per gallon...
 3.2.77: What is a polynomial function?
 3.2.78: What do we mean when we describe the graph of a polynomial function...
 3.2.79: What is meant by the end behavior of a polynomial function?
 3.2.80: Explain how to use the Leading Coefficient Test to determine the en...
 3.2.81: Why is a thirddegree polynomial function with a negative leading c...
 3.2.82: What are the zeros of a polynomial function and how are they found?
 3.2.83: Explain the relationship between the multiplicity of a zero and whe...
 3.2.84: If f is a polynomial function, and f(a) a nd [(b) have opposite sig...
 3.2.85: Explain the relationship between the degree of a polynomial functio...
 3.2.86: Can the graph of a polynomial function have no xintercepts? Explain.
 3.2.87: Can the graph of a polynomial function have no yintercept? Explain.
 3.2.88: Describe a strategy for graphing a polynomial function. In your des...
 3.2.89: Use a graphing utility to verify any five of the graphs that you dr...
 3.2.90: Write a polynomial function that imitates the end behavior of each ...
 3.2.91: Write a polynomial function that imitates the end behavior of each ...
 3.2.92: Write a polynomial function that imitates the end behavior of each ...
 3.2.93: Write a polynomial function that imitates the end behavior of each ...
 3.2.94: In Exercises 9497, use a graphing utility with a viewing rectangle...
 3.2.95: In Exercises 9497, use a graphing utility with a viewing rectangle...
 3.2.96: In Exercises 9497, use a graphing utility with a viewing rectangle...
 3.2.97: In Exercises 9497, use a graphing utility with a viewing rectangle...
 3.2.98: In Exercises 9899~ use a graphing utility to graph f and gin the s...
 3.2.99: In Exercises 9899~ use a graphing utility to graph f and gin the s...
 3.2.100: In Exercises 100103, detennine whether each statemelll makes sens...
 3.2.101: In Exercises 100103, detennine whether each statemelll makes sens...
 3.2.102: In Exercises 100103, detennine whether each statemelll makes sens...
 3.2.103: In Exercises 100103, detennine whether each statemelll makes sens...
 3.2.104: In Exercises 104107. determine whether each statement is true or f...
 3.2.105: In Exercises 104107. determine whether each statement is true or f...
 3.2.106: In Exercises 104107. determine whether each statement is true or f...
 3.2.107: In Exercises 104107. determine whether each statement is true or f...
 3.2.108: Use the descriptions in Exerrcises 108109 to write 110. Divide 737...
 3.2.109: Use the descriptions in Exerrcises 108109 to write 110. Divide 737...
 3.2.110: Exercises 110112 will help you prepare for tire matedal c.overed ...
 3.2.111: Exercises 110112 will help you prepare for tire matedal c.overed ...
 3.2.112: Exercises 110112 will help you prepare for tire matedal c.overed ...
Solutions for Chapter 3.2: Polynomial Functions and Their Graphs
Full solutions for College Algebra  6th Edition
ISBN: 9780321782281
Solutions for Chapter 3.2: Polynomial Functions and Their Graphs
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9780321782281. This textbook survival guide was created for the textbook: College Algebra , edition: 6. Since 112 problems in chapter 3.2: Polynomial Functions and Their Graphs have been answered, more than 39231 students have viewed full stepbystep solutions from this chapter. Chapter 3.2: Polynomial Functions and Their Graphs includes 112 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Iterative method.
A sequence of steps intended to approach the desired solution.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Outer product uv T
= column times row = rank one matrix.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.