 4.6.1: Solve the inequality 3  4x 7 5. Graph the solution set. (pp. A76 A77)
 4.6.2: Solve the inequality x2  5x 24. Graph the solution set. (pp. 168 171)
 4.6.3: A test number for the interval 2 6 x 6 5 could be 4.
 4.6.4: The graph of f1x2 = x x  3 is above the x axis for x 6 0 or x 7 3...
 4.6.5: In 5 8, use the graph of the function f to solve the inequality.
 4.6.6: In 5 8, use the graph of the function f to solve the inequality.
 4.6.7: In 5 8, use the graph of the function f to solve the inequality.
 4.6.8: In 5 8, use the graph of the function f to solve the inequality.
 4.6.9: In 914, solve the inequality by using the graph of the function.
 4.6.10: In 914, solve the inequality by using the graph of the function.
 4.6.11: In 914, solve the inequality by using the graph of the function.
 4.6.12: In 914, solve the inequality by using the graph of the function.
 4.6.13: In 914, solve the inequality by using the graph of the function.
 4.6.14: In 914, solve the inequality by using the graph of the function.
 4.6.15: In 1518, solve the inequality by using the graph of the function.
 4.6.16: In 1518, solve the inequality by using the graph of the function.
 4.6.17: In 1518, solve the inequality by using the graph of the function.
 4.6.18: In 1518, solve the inequality by using the graph of the function.
 4.6.19: In 1948, solve each inequality algebraically.
 4.6.20: In 1948, solve each inequality algebraically.
 4.6.21: In 1948, solve each inequality algebraically.
 4.6.22: In 1948, solve each inequality algebraically.
 4.6.23: In 1948, solve each inequality algebraically.
 4.6.24: In 1948, solve each inequality algebraically.
 4.6.25: In 1948, solve each inequality algebraically.
 4.6.26: In 1948, solve each inequality algebraically.
 4.6.27: In 1948, solve each inequality algebraically.
 4.6.28: In 1948, solve each inequality algebraically.
 4.6.29: In 1948, solve each inequality algebraically.
 4.6.30: In 1948, solve each inequality algebraically.
 4.6.31: In 1948, solve each inequality algebraically.
 4.6.32: In 1948, solve each inequality algebraically.
 4.6.33: In 1948, solve each inequality algebraically.
 4.6.34: In 1948, solve each inequality algebraically.
 4.6.35: In 1948, solve each inequality algebraically.
 4.6.36: In 1948, solve each inequality algebraically.
 4.6.37: In 1948, solve each inequality algebraically.
 4.6.38: In 1948, solve each inequality algebraically.
 4.6.39: In 1948, solve each inequality algebraically.
 4.6.40: In 1948, solve each inequality algebraically.
 4.6.41: In 1948, solve each inequality algebraically.
 4.6.42: In 1948, solve each inequality algebraically.
 4.6.43: In 1948, solve each inequality algebraically.
 4.6.44: In 1948, solve each inequality algebraically.
 4.6.45: In 1948, solve each inequality algebraically.
 4.6.46: In 1948, solve each inequality algebraically.
 4.6.47: In 1948, solve each inequality algebraically.
 4.6.48: In 1948, solve each inequality algebraically.
 4.6.49: In 4960, solve each inequality algebraically.
 4.6.50: In 4960, solve each inequality algebraically.
 4.6.51: In 4960, solve each inequality algebraically.
 4.6.52: In 4960, solve each inequality algebraically.
 4.6.53: In 4960, solve each inequality algebraically.
 4.6.54: In 4960, solve each inequality algebraically.
 4.6.55: In 4960, solve each inequality algebraically.
 4.6.56: In 4960, solve each inequality algebraically.
 4.6.57: In 4960, solve each inequality algebraically.
 4.6.58: In 4960, solve each inequality algebraically.
 4.6.59: In 4960, solve each inequality algebraically.
 4.6.60: In 4960, solve each inequality algebraically.
 4.6.61: In 61 and 62 (a) find the zeros of each function,(b) factor each fu...
 4.6.62: In 61 and 62 (a) find the zeros of each function,(b) factor each fu...
 4.6.63: In 6366, (a) graph each function by hand, and (b) solve f1x2 0
 4.6.64: In 6366, (a) graph each function by hand, and (b) solve f1x2 1
 4.6.65: In 6366, (a) graph each function by hand, and (b) solve f1x2 2
 4.6.66: In 6366, (a) graph each function by hand, and (b) solve f1x2 3
 4.6.67: For what positive numbers will the cube of a number exceed four tim...
 4.6.68: For what positive numbers will the cube of a number be less than th...
 4.6.69: What is the domain of the function f1x2 = 2x4  16?
 4.6.70: What is the domain of the function f1x2 = 2x3  3x2 ?
 4.6.71: What is the domain of the function f1x2 = A x  2 x + 4 ?
 4.6.72: What is the domain of the function f1x2 = A x  1 x + 4 ?
 4.6.73: In 7376, determine where the graph of f is below the graph of g by ...
 4.6.74: In 7376, determine where the graph of f is below the graph of g by ...
 4.6.75: In 7376, determine where the graph of f is below the graph of g by ...
 4.6.76: In 7376, determine where the graph of f is below the graph of g by ...
 4.6.77: Suppose that the daily cost C of manufacturing bicycles is given by...
 4.6.78: 77. Suppose that the government imposes a $1000 per day tax on the ...
 4.6.79: Originating on Pentecost Island in the Pacific, the practice of a p...
 4.6.80: According to Newtons Law of universal gravitation, the attractive f...
 4.6.81: Mrs. West has decided to take her fifth grade class to a play. The ...
 4.6.82: Make up an inequality that has no solution. Make up one that has ex...
 4.6.83: The inequality x4 + 1 6 5 has no solution. Explain why.
 4.6.84: A student attempted to solve the inequality x + 4 x  3 0 by multip...
 4.6.85: Write a rational inequality whose solution set is {x 3 6 x 5}.
Solutions for Chapter 4.6: Polynomial and Rational Inequalities
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 4.6: Polynomial and Rational Inequalities
Get Full SolutionsChapter 4.6: Polynomial and Rational Inequalities includes 85 full stepbystep solutions. Since 85 problems in chapter 4.6: Polynomial and Rational Inequalities have been answered, more than 126930 students have viewed full stepbystep solutions from this chapter. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6.

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

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

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.

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.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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

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.