 3.4.1: Sketch the graph of y = 1x
 3.4.2: Sketch the graph of y =1/x
 3.4.3: List the intercepts of the equation y =x38
 3.4.4: The function is decreasing on the intervalf1x2 = x2
 3.4.5: When functions are defined by more than one equation, they are call...
 3.4.6: True or False The cube function is odd and is increasing on the int...
 3.4.7: True or False The cube root function is odd and is decreasing on th...
 3.4.8: True or False The domain and the range of the reciprocal function a...
 3.4.9: In 916, match each graph to its function. A. Constant function B. I...
 3.4.10: In 916, match each graph to its function. A. Constant function B. I...
 3.4.11: In 916, match each graph to its function. A. Constant function B. I...
 3.4.12: In 916, match each graph to its function. A. Constant function B. I...
 3.4.13: In 916, match each graph to its function. A. Constant function B. I...
 3.4.14: In 916, match each graph to its function. A. Constant function B. I...
 3.4.15: In 916, match each graph to its function. A. Constant function B. I...
 3.4.16: In 916, match each graph to its function. A. Constant function B. I...
 3.4.17: In 1724,sketch the graph of each function. Be sure to label three p...
 3.4.18: In 1724,sketch the graph of each function. Be sure to label three p...
 3.4.19: In 1724,sketch the graph of each function. Be sure to label three p...
 3.4.20: In 1724,sketch the graph of each function. Be sure to label three p...
 3.4.21: In 1724,sketch the graph of each function. Be sure to label three p...
 3.4.22: In 1724,sketch the graph of each function. Be sure to label three p...
 3.4.23: In 1724,sketch the graph of each function. Be sure to label three p...
 3.4.24: In 1724,sketch the graph of each function. Be sure to label three p...
 3.4.25: 2 f1x2 = c x2 if x 6 0 2 if x = 0 2x + 1 if x 7 0find: (a)f122 (b)...
 3.4.26: f find: (a) f122 (b) f112 (c) f102 f1x2 = c 3x if x 6 1 0 if x ...
 3.4.27: x2 = e 2x  4 if 1 x 2 x3  2 if 2 6 x 3find: (a) (b) (c) (d)
 3.4.28: 3) f1x2 = e x3 if 2 x 6 1 3x + 2 if 1 x 4find: (a) (b) (c) (d)
 3.4.29: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.30: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.31: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.32: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.33: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.34: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.35: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.36: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.37: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.38: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.39: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.40: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 3.4.41: In 4144, the graph of a piecewisedefined function is given.Write a...
 3.4.42: In 4144, the graph of a piecewisedefined function is given.Write a...
 3.4.43: In 4144, the graph of a piecewisedefined function is given.Write a...
 3.4.44: In 4144, the graph of a piecewisedefined function is given.Write a...
 3.4.45: If find (a) f11.22 (b) f11.62 (c) f11.82
 3.4.46: If find (a) f11.22 (b) f11.62 (c) f11.82
 3.4.47: Cell Phone Service Sprint PCS offers a monthly cellular phone plan ...
 3.4.48: Parking at OHare International Airport The shortterm (no more than...
 3.4.49: Cost of Natural Gas In April 2009, Peoples Energy had the following...
 3.4.50: Cost of Natural Gas In April 2009, Nicor Gas had the following rate...
 3.4.51: Federal Income Tax Two 2009 Tax Rate Schedules are given in the acc...
 3.4.52: Federal Income Tax Refer to the revised 2009 tax rate schedules. If...
 3.4.53: Cost of Transporting Goods A trucking company transports goods betw...
 3.4.54: Car Rental Costs An economy car rented in Florida from National Car...
 3.4.55: Minimum Payments for Credit Cards Holders of credit cards issued by...
 3.4.56: Interest Payments for Credit Cards Refer to 55. The card holder may...
 3.4.57: Wind Chill The wind chill factor represents the equivalent air temp...
 3.4.58: Wind Chill Redo 57(a)(d) for an air temperature10C
 3.4.59: Firstclass Mail In 2009 the U.S. Postal Service charged $1.17 post...
 3.4.60: In 6067, use a graphing utilityExploration Graph Then on the same s...
 3.4.61: In 6067, use a graphing utilityExploration Graph Then on the same s...
 3.4.62: In 6067, use a graphing utilityExploration Graph Then on the same s...
 3.4.63: In 6067, use a graphing utilityExploration Graph Then on the same s...
 3.4.64: In 6067, use a graphing utilityExploration Graph Then on the same s...
 3.4.65: In 6067, use a graphing utilityExploration Graph Then on the same s...
 3.4.66: In 6067, use a graphing utilityExploration Graph and on the same sc...
 3.4.67: In 6067, use a graphing utilityExploration Graph and on the same sc...
 3.4.68: onsider the equation Is this a function? What is its domain? What i...
 3.4.69: Define some functions that pass through and and are increasing for ...
Solutions for Chapter 3.4: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 3.4
Get Full SolutionsChapter 3.4 includes 69 full stepbystep solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. This expansive textbook survival guide covers the following chapters and their solutions. Since 69 problems in chapter 3.4 have been answered, more than 55710 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9.

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

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

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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

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

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.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

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

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.