 3.1.1: The inequality can be written in interval notation as
 3.1.2: If the value of the expression
 3.1.3: The inequality can be written in interval notation as1 6 x 6 3
 3.1.4: If the value of the expression3x2  5x + 1 x
 3.1.5: The domain of the variable in the expressionx  3 x + 4
 3.1.6: Solve the inequality: Graph the solution set3  2x 7 5.
 3.1.7: If is a function defined by the equation then x is called the varia...
 3.1.8: The set of all images of the elements in the domain of a function i...
 3.1.9: If the domain of is all real numbers in the interval and the domain...
 3.1.10: The domain of consists of numbers x for which g1x2 0 that are in th...
 3.1.11: If and thenf1x2 = x + 1 g1x2 = x = 3 f1x2 = x + 1 , x3  1x + 12.
 3.1.12: True or False Every relation is a function.
 3.1.13: True or False The domain of consists of the numbers x that are in t...
 3.1.14: True or False The independent variable is sometimes referred to as ...
 3.1.15: True or False If no domain is specified for a function then the dom...
 3.1.16: True or False The domain of the functionis 5x x Z ;26. f1x2 = x2  4 x
 3.1.17: In 1526, determine whether each relation represents a function. For...
 3.1.18: In 1526, determine whether each relation represents a function. For...
 3.1.19: In 1526, determine whether each relation represents a function. For...
 3.1.20: In 1526, determine whether each relation represents a function. For...
 3.1.21: In 1526, determine whether each relation represents a function. For...
 3.1.22: In 1526, determine whether each relation represents a function. For...
 3.1.23: In 1526, determine whether each relation represents a function. For...
 3.1.24: In 1526, determine whether each relation represents a function. For...
 3.1.25: In 1526, determine whether each relation represents a function. For...
 3.1.26: In 1526, determine whether each relation represents a function. For...
 3.1.27: In 1526, determine whether each relation represents a function. For...
 3.1.28: In 1526, determine whether each relation represents a function. For...
 3.1.29: In 2738, determine whether the equation defines y as a function of ...
 3.1.30: In 2738, determine whether the equation defines y as a function of ...
 3.1.31: In 2738, determine whether the equation defines y as a function of ...
 3.1.32: In 2738, determine whether the equation defines y as a function of ...
 3.1.33: In 2738, determine whether the equation defines y as a function of ...
 3.1.34: In 2738, determine whether the equation defines y as a function of ...
 3.1.35: In 2738, determine whether the equation defines y as a function of ...
 3.1.36: In 2738, determine whether the equation defines y as a function of ...
 3.1.37: In 2738, determine whether the equation defines y as a function of ...
 3.1.38: In 2738, determine whether the equation defines y as a function of ...
 3.1.39: In 2738, determine whether the equation defines y as a function of ...
 3.1.40: In 2738, determine whether the equation defines y as a function of ...
 3.1.41: In 3946, find the following for each function: (a) f102 (b) f112 (c...
 3.1.42: In 3946, find the following for each function: (a) f102 (b) f112 (c...
 3.1.43: In 3946, find the following for each function: (a) f102 (b) f112 (c...
 3.1.44: In 3946, find the following for each function: (a) f102 (b) f112 (c...
 3.1.45: In 3946, find the following for each function: (a) f102 (b) f112 (c...
 3.1.46: In 3946, find the following for each function: (a) f102 (b) f112 (c...
 3.1.47: In 3946, find the following for each function: (a) f102 (b) f112 (c...
 3.1.48: In 3946, find the following for each function: (a) f102 (b) f112 (c...
 3.1.49: In 4762, find the domain of each function. f1x2 = 5x + 4
 3.1.50: In 4762, find the domain of each function. f1x2 = x2 + 2
 3.1.51: In 4762, find the domain of each function. f1x2 = xx2 + 1
 3.1.52: In 4762, find the domain of each function. f1x2 = x2x2 + 1
 3.1.53: In 4762, find the domain of each function. g1x2 = xx2  16
 3.1.54: In 4762, find the domain of each function. h1x2 = 2xx2  4
 3.1.55: In 4762, find the domain of each function. F1x2 = x  2x3 + x
 3.1.56: In 4762, find the domain of each function. G1x2 = x + 4x3  4x
 3.1.57: In 4762, find the domain of each function. h1x2 = 23x  12
 3.1.58: In 4762, find the domain of each function. G1x2 = 21  x
 3.1.59: In 4762, find the domain of each function. f1x2 = 42x  9
 3.1.60: In 4762, find the domain of each function. f1x2 = x2x  4
 3.1.61: In 4762, find the domain of each function. p1x2 = A2x  1
 3.1.62: In 4762, find the domain of each function. q1x2 = 2x  2
 3.1.63: In 4762, find the domain of each function. P(t) = 2t  43t  21
 3.1.64: In 4762, find the domain of each function. h(z) = 2z + 3z  2
 3.1.65: In 6372, for the given functions and g, find the following. For par...
 3.1.66: In 6372, for the given functions and g, find the following. For par...
 3.1.67: In 6372, for the given functions and g, find the following. For par...
 3.1.68: In 6372, for the given functions and g, find the following. For par...
 3.1.69: In 6372, for the given functions and g, find the following. For par...
 3.1.70: In 6372, for the given functions and g, find the following. For par...
 3.1.71: In 6372, for the given functions and g, find the following. For par...
 3.1.72: In 6372, for the given functions and g, find the following. For par...
 3.1.73: In 6372, for the given functions and g, find the following. For par...
 3.1.74: In 6372, for the given functions and g, find the following. For par...
 3.1.75: Given and find the function g. 1f + g21x2 = 6  1 2 f1x2 = 3x + 1 x
 3.1.76: Given and a find the function g. f g b1x2 = x + 1 x2  x f1x2 = , 1 x
 3.1.77: In 7582, find the difference quotient of that is, find f1x + h2  f...
 3.1.78: In 7582, find the difference quotient of that is, find f1x + h2  f...
 3.1.79: In 7582, find the difference quotient of that is, find f1x + h2  f...
 3.1.80: In 7582, find the difference quotient of that is, find f1x + h2  f...
 3.1.81: In 7582, find the difference quotient of that is, find f1x + h2  f...
 3.1.82: In 7582, find the difference quotient of that is, find f1x + h2  f...
 3.1.83: In 7582, find the difference quotient of that is, find f1x + h2  f...
 3.1.84: In 7582, find the difference quotient of that is, find f1x + h2  f...
 3.1.85: If and what is the value of A?f1x2 = 2x f122 = 5, 3 + Ax2 + 4x  5
 3.1.86: If and what is the value of B?f1x2 = 3x f112 = 12
 3.1.87: If and what is the value of A?f1x2 = f102 = 2, 3x + 8 2x  A
 3.1.88: If and what is the value of B?f1x2 = , 2x  B 3x + 4
 3.1.89: . If and what is the value of A? Where is not defined?f1x2 = f142 =...
 3.1.90: If and is undefined, what are the values of A and B?f1x2 = f112 x ...
 3.1.91: Geometry Express the area A of a rectangle as a function of the len...
 3.1.92: Geometry Express the area A of an isosceles right triangle as a fun...
 3.1.93: Constructing Functions Express the gross salary G of a person who e...
 3.1.94: Constructing Functions Tiffany, a commissioned salesperson, earns $...
 3.1.95: Population as a Function of Age The function represents the populat...
 3.1.96: Number of Rooms The function represents the number N of housing uni...
 3.1.97: Effect of Gravity on Earth If a rock falls from a height of 20 mete...
 3.1.98: Effect of Gravity on Jupiter If a rock falls from a height of 20 me...
 3.1.99: Cost of TransAtlantic Travel A Boeing 747 crosses the Atlantic Oce...
 3.1.100: CrosssectionalArea The crosssectional area of a beam cut from a l...
 3.1.101: Economics The participation rate is the number of people in the lab...
 3.1.102: Crimes Suppose that represents the number of violent crimes committ...
 3.1.103: Health Care Suppose that P x represents the percentage of income sp...
 3.1.104: Income Tax Suppose that represents the income of an individual in y...
 3.1.105: Profit Function Suppose thatthe revenue R,in dollars,from selling x...
 3.1.106: Profit Function Suppose that the revenue R, in dollars, from sellin...
 3.1.107: Some functions have the property that for all real numbers a and b....
 3.1.108: Are the functions and the same? Explain.f1x2 = x  1 g1x2 = x2  1x...
 3.1.109: Investigate when, historically, the use of the function notation y ...
 3.1.110: Find a function H that multiplies a number x by 3, then subtracts t...
Solutions for Chapter 3.1: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 3.1
Get Full SolutionsSince 110 problems in chapter 3.1 have been answered, more than 55449 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Chapter 3.1 includes 110 full stepbystep solutions.

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

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.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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.

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

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

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).

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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).

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

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.