 3.6.3.6.1: Graph each piecewisedefined function. See Examples 1 and 2.f 1x2 =...
 3.6.3.6.2: Graph each piecewisedefined function. See Examples 1 and 2.f 1x2 =...
 3.6.3.6.3: Graph each piecewisedefined function. See Examples 1 and 2.f 1x2 =...
 3.6.3.6.4: Graph each piecewisedefined function. See Examples 1 and 2.f 1x2 =...
 3.6.3.6.5: Graph each piecewisedefined function. See Examples 1 and 2.g1x2 = ...
 3.6.3.6.6: Graph each piecewisedefined function. See Examples 1 and 2.g1x2 = ...
 3.6.3.6.7: Graph each piecewisedefined function. See Examples 1 and 2.f 1x2 =...
 3.6.3.6.8: Graph each piecewisedefined function. See Examples 1 and 2.f 1x2 =...
 3.6.3.6.9: (Sections 3.2, 3.6) Graph each piecewisedefined function. Use the ...
 3.6.3.6.10: (Sections 3.2, 3.6) Graph each piecewisedefined function. Use the ...
 3.6.3.6.11: (Sections 3.2, 3.6) Graph each piecewisedefined function. Use the ...
 3.6.3.6.12: (Sections 3.2, 3.6) Graph each piecewisedefined function. Use the ...
 3.6.3.6.13: (Sections 3.2, 3.6) Graph each piecewisedefined function. Use the ...
 3.6.3.6.14: (Sections 3.2, 3.6) Graph each piecewisedefined function. Use the ...
 3.6.3.6.15: (Sections 3.2, 3.6) Graph each piecewisedefined function. Use the ...
 3.6.3.6.16: (Sections 3.2, 3.6) Graph each piecewisedefined function. Use the ...
 3.6.3.6.17: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 0 x ...
 3.6.3.6.18: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 0 x ...
 3.6.3.6.19: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 1x  2
 3.6.3.6.20: Sketch the graph of function. See Examples 3 through 6. f 1x2 = 1x + 3
 3.6.3.6.21: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 0 x  4
 3.6.3.6.22: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 0 x ...
 3.6.3.6.23: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 1x + 2
 3.6.3.6.24: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 1x  2
 3.6.3.6.25: Sketch the graph of function. See Examples 3 through 6.y = 1x  422
 3.6.3.6.26: Sketch the graph of function. See Examples 3 through 6.y = 1x + 422
 3.6.3.6.27: Sketch the graph of function. See Examples 3 through 6.f 1x2 = x2 + 4
 3.6.3.6.28: Sketch the graph of function. See Examples 3 through 6.f 1x2 = x2  4
 3.6.3.6.29: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 1x ...
 3.6.3.6.30: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 1x ...
 3.6.3.6.31: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 0 x ...
 3.6.3.6.32: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 0 x ...
 3.6.3.6.33: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 1x +...
 3.6.3.6.34: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 1x +...
 3.6.3.6.35: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 0 x ...
 3.6.3.6.36: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 0 x ...
 3.6.3.6.37: Sketch the graph of function. See Examples 3 through 6.g1x2 = 1x  ...
 3.6.3.6.38: Sketch the graph of function. See Examples 3 through 6.h1x2 = 1x + ...
 3.6.3.6.39: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 1x +...
 3.6.3.6.40: Sketch the graph of function. See Examples 3 through 6.f 1x2 = 1x +...
 3.6.3.6.41: Sketch the graph of each function. See Examples 3 through 7. f 1x2 ...
 3.6.3.6.42: Sketch the graph of each function. See Examples 3 through 7.g1x2 = ...
 3.6.3.6.43: Sketch the graph of each function. See Examples 3 through 7.h1x2 = ...
 3.6.3.6.44: Sketch the graph of each function. See Examples 3 through 7. f 1x2 ...
 3.6.3.6.45: Sketch the graph of each function. See Examples 3 through 7.h1x2 = ...
 3.6.3.6.46: Sketch the graph of each function. See Examples 3 through 7.g1x2 = ...
 3.6.3.6.47: Sketch the graph of each function. See Examples 3 through 7. f 1x2 ...
 3.6.3.6.48: Sketch the graph of each function. See Examples 3 through 7.f 1x2 =...
 3.6.3.6.49: Match each equation with its graph. See Section 3.3.y = 1
 3.6.3.6.50: Match each equation with its graph. See Section 3.3.x = 1
 3.6.3.6.51: Match each equation with its graph. See Section 3.3.x = 3
 3.6.3.6.52: Match each equation with its graph. See Section 3.3.y = 3
 3.6.3.6.53: Draw a graph whose domain is 1, 5] and whose range is [2, 2.
 3.6.3.6.54: In your own words, describe how to graph a piecewisedefined function.
 3.6.3.6.55: Graph: f 1x2 =  12x if x 0x + 1 if 0 6 x 22x  1 if x 7 2
 3.6.3.6.56: Graph: f 1x2 =  13x if x 0x + 2 if 0 6 x 43x  4 if x 7 4
 3.6.3.6.57: Write the domain and range of the following exercisesExercise 29
 3.6.3.6.58: Write the domain and range of the following exercisesExercise 30
 3.6.3.6.59: Write the domain and range of the following exercisesExercise 45
 3.6.3.6.60: Write the domain and range of the following exercisesExercise 46
 3.6.3.6.61: Without graphing, find the domain of each function.f 1x2 = 51x  20...
 3.6.3.6.62: Without graphing, find the domain of each function.g1x2 = 31x + 5
 3.6.3.6.63: Without graphing, find the domain of each function.h1x2 = 5 0 x  2...
 3.6.3.6.64: Without graphing, find the domain of each function.f 1x2 = 3 0 x +...
 3.6.3.6.65: Without graphing, find the domain of each function.g1x2 = 9  1x + 103
 3.6.3.6.66: Without graphing, find the domain of each function.h1x2 = 1x  17  3
 3.6.3.6.67: Sketch the graph of each piecewisedefined function. Write the doma...
 3.6.3.6.68: Sketch the graph of each piecewisedefined function. Write the doma...
 3.6.3.6.69: Sketch the graph of each piecewisedefined function. Write the doma...
 3.6.3.6.70: Sketch the graph of each piecewisedefined function. Write the doma...
Solutions for Chapter 3.6: Graphing PiecewiseDefined Functions and Shifting and Reflecting Graphs of Functions
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 3.6: Graphing PiecewiseDefined Functions and Shifting and Reflecting Graphs of Functions
Get Full SolutionsSince 70 problems in chapter 3.6: Graphing PiecewiseDefined Functions and Shifting and Reflecting Graphs of Functions have been answered, more than 66759 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.6: Graphing PiecewiseDefined Functions and Shifting and Reflecting Graphs of Functions includes 70 full stepbystep solutions. This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

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

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

Iterative method.
A sequence of steps intended to approach the desired solution.

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.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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 equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

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