 3.6.1: Fill in each blank so that the resulting statement is true.We solve...
 3.6.2: Fill in each blank so that the resulting statement is true.The poin...
 3.6.3: Fill in each blank so that the resulting statement is true.True or ...
 3.6.4: Fill in each blank so that the resulting statement is true.True or ...
 3.6.5: Fill in each blank so that the resulting statement is true.Consider...
 3.6.6: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.7: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.8: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.9: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.10: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.11: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.12: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.13: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.14: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.15: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.16: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.17: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.18: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.19: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.20: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.21: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.22: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.23: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.24: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.25: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.26: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.27: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.28: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.29: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.30: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.31: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.32: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.33: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.34: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.35: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.36: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.37: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.38: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.39: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.40: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.41: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.42: Solve each polynomial inequality in Exercises 142 and graph thesolu...
 3.6.43: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.44: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.45: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.46: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.47: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.48: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.49: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.50: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.51: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.52: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.53: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.54: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.55: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.56: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.57: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.58: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.59: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.60: Solve each rational inequality in Exercises 4360 and graph thesolut...
 3.6.61: In Exercises 6164, find the domain of each function.f(x) = 22x2  5...
 3.6.62: In Exercises 6164, find the domain of each function.f(x) = 124x2  ...
 3.6.63: In Exercises 6164, find the domain of each function.f(x) = A2xx + 1...
 3.6.64: In Exercises 6164, find the domain of each function.f(x) = Ax2x  1...
 3.6.65: Solve each inequality in Exercises 6570 and graph the solutionset o...
 3.6.66: Solve each inequality in Exercises 6570 and graph the solutionset o...
 3.6.67: Solve each inequality in Exercises 6570 and graph the solutionset o...
 3.6.68: Solve each inequality in Exercises 6570 and graph the solutionset o...
 3.6.69: Solve each inequality in Exercises 6570 and graph the solutionset o...
 3.6.70: Solve each inequality in Exercises 6570 and graph the solutionset o...
 3.6.71: In Exercises 7172, use the graph of the polynomial function tosolve...
 3.6.72: In Exercises 7172, use the graph of the polynomial function tosolve...
 3.6.73: In Exercises 7374, use the graph of the rational function to solvee...
 3.6.74: In Exercises 7374, use the graph of the rational function to solvee...
 3.6.75: Use the position functions(t) = 16t2 + v0 t + s0(v0 = initial velo...
 3.6.76: Use the position functions(t) = 16t2 + v0 t + s0(v0 = initial velo...
 3.6.77: Use the position functions(t) = 16t2 + v0 t + s0(v0 = initial velo...
 3.6.78: Use the position functions(t) = 16t2 + v0 t + s0(v0 = initial velo...
 3.6.79: The perimeter of a rectangle is 50 feet. Describe the possiblelengt...
 3.6.80: The perimeter of a rectangle is 180 feet. Describe the possibleleng...
 3.6.81: What is a polynomial inequality?
 3.6.82: What is a rational inequality?
 3.6.83: If f is a polynomial or rational function, explain how thegraph of ...
 3.6.84: Use a graphing utility to verify your solution sets to any threeof ...
 3.6.85: Use a graphing utility to verify your solution sets to any threeof ...
 3.6.86: Solve each inequality in Exercises 8691 using a graphing utility.x2...
 3.6.87: Solve each inequality in Exercises 8691 using a graphing utility.2x...
 3.6.88: Solve each inequality in Exercises 8691 using a graphing utility.x3...
 3.6.89: Solve each inequality in Exercises 8691 using a graphing utility.x ...
 3.6.90: Solve each inequality in Exercises 8691 using a graphing utility.x ...
 3.6.91: Solve each inequality in Exercises 8691 using a graphing utility.1x...
 3.6.92: The graph shows stopping distances for trucks at various speedson d...
 3.6.93: The graph shows stopping distances for trucks at various speedson d...
 3.6.94: In Exercises 9497, determine whether eachstatement makes sense or d...
 3.6.95: In Exercises 9497, determine whether eachstatement makes sense or d...
 3.6.96: In Exercises 9497, determine whether eachstatement makes sense or d...
 3.6.97: In Exercises 9497, determine whether eachstatement makes sense or d...
 3.6.98: In Exercises 98101, determine whether each statement is true orfals...
 3.6.99: In Exercises 98101, determine whether each statement is true orfals...
 3.6.100: In Exercises 98101, determine whether each statement is true orfals...
 3.6.101: In Exercises 98101, determine whether each statement is true orfals...
 3.6.102: Write a polynomial inequality whose solution set is[3, 5].
 3.6.103: Write a rational inequality whose solution set is( , 4) [3, ).
 3.6.104: In Exercises 104107, use inspection to describe each inequalityssol...
 3.6.105: In Exercises 104107, use inspection to describe each inequalityssol...
 3.6.106: In Exercises 104107, use inspection to describe each inequalityssol...
 3.6.107: In Exercises 104107, use inspection to describe each inequalityssol...
 3.6.108: The graphing utility screen shows the graph ofy = 4x2  8x + 7.a. U...
 3.6.109: The graphing utility screen shows the graph ofy = 227  3x2. Write ...
 3.6.110: The size of a television screen refers to the length of itsdiagonal...
 3.6.111: Find the domain of h(x) = 236  2x.(Section 2.6, Example 1)
 3.6.112: Use the graph of y = f(x) to graph y = f(x) + 3.
 3.6.113: Exercises 113115 will help you prepare for the material coveredin t...
 3.6.114: Exercises 113115 will help you prepare for the material coveredin t...
 3.6.115: Exercises 113115 will help you prepare for the material coveredin t...
Solutions for Chapter 3.6: Polynomial and Rational Inequalities
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 3.6: Polynomial and Rational Inequalities
Get Full SolutionsSince 115 problems in chapter 3.6: Polynomial and Rational Inequalities have been answered, more than 29842 students have viewed full stepbystep solutions from this chapter. Chapter 3.6: Polynomial and Rational Inequalities includes 115 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 7. College Algebra was written by and is associated to the ISBN: 9780134469164.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Column space C (A) =
space of all combinations of the columns of A.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib IIĀ· Condition numbers measure the sensitivity of the output to change in the input.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.