 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 53684 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.

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

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

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.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

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 II· Condition numbers measure the sensitivity of the output to change in the input.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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).

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Solvable system Ax = b.
The right side b is in the column space of A.

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

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.