 2.4.1: Sketch the graph of y = 1x. (p. 22)
 2.4.2: Sketch the graph of y = 1 x . (pp. 2223)
 2.4.3: List the intercepts of the equation y = x3  8. (pp. 1819)
 2.4.4: The function f1x2 = x2 is decreasing on the interval _________.
 2.4.5: When functions are defined by more than one equation, they are call...
 2.4.6: The cube function is odd and is increasing on the interval 1  , 2.
 2.4.7: The cube root function is odd and is decreasing on the interval 1 ...
 2.4.8: The domain and the range of the reciprocal function are the set of ...
 2.4.9: In 9 16, match each graph to its function.
 2.4.10: In 9 16, match each graph to its function.
 2.4.11: In 9 16, match each graph to its function.
 2.4.12: In 9 16, match each graph to its function.
 2.4.13: In 9 16, match each graph to its function.
 2.4.14: In 9 16, match each graph to its function.
 2.4.15: In 9 16, match each graph to its function.
 2.4.16: In 9 16, match each graph to its function.
 2.4.17: In 1724, sketch the graph of each function. Be sure to label three ...
 2.4.18: In 1724, sketch the graph of each function. Be sure to label three ...
 2.4.19: In 1724, sketch the graph of each function. Be sure to label three ...
 2.4.20: In 1724, sketch the graph of each function. Be sure to label three ...
 2.4.21: In 1724, sketch the graph of each function. Be sure to label three ...
 2.4.22: In 1724, sketch the graph of each function. Be sure to label three ...
 2.4.23: In 1724, sketch the graph of each function. Be sure to label three ...
 2.4.24: In 1724, sketch the graph of each function. Be sure to label three ...
 2.4.25: If f1x2 = c x2 if x 6 0 2 if x = 0 2x + 1 if x 7 0 find: (a) f1 22...
 2.4.26: If f1x2 = c 3x if x 6 1 0 if x = 1 2x2 + 1 if x 7 1
 2.4.27: f f1x2 = e 2x  4 if 1 x 2 x3  2 if 2 6 x 3 find: (a) f102 (b) f1...
 2.4.28: If f1x2 = e x3 if 2 x 6 1 3x + 2 if 1 x 4 find: (a) f1 12 (b) f10...
 2.4.29: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.30: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.31: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.32: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.33: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.34: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.35: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.36: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.37: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.38: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.39: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.40: In 2940: (a) Find the domain of each function. (b) Locate any inter...
 2.4.41: In 4144, the graph of a piecewisedefined function is given. Write ...
 2.4.42: In 4144, the graph of a piecewisedefined function is given. Write ...
 2.4.43: In 4144, the graph of a piecewisedefined function is given. Write ...
 2.4.44: In 4144, the graph of a piecewisedefined function is given. Write ...
 2.4.45: If f1x2 = int12x2, find (a) f11.22 (b) f11.62 (c) f1 1.82
 2.4.46: If f1x2 = inta x 2 b, find (a) f11.22 (b) f11.62 (c) f1 1.82
 2.4.47: Sprint PCS offers a monthly cellular phone plan for $39.99. It incl...
 2.4.48: The shortterm (no more than 24 hours) parking fee F (in dollars) f...
 2.4.49: In March 2011, Peoples Energy had the following rate schedule for n...
 2.4.50: In March 2011, Nicor Gas had the following rate schedule for natura...
 2.4.51: Two 2011 Tax Rate Schedules are given in the table below. If x equa...
 2.4.52: Refer to the revised 2011 tax rate schedules. If x equals taxable i...
 2.4.53: A trucking company transports goods between Chicago and New York, a...
 2.4.54: An economy car rented in Florida from National Car Rental on a week...
 2.4.55: Fannie Mae charges an adverse market delivery charge on all mortgag...
 2.4.56: Holders of credit cards issued by banks, department stores, oil com...
 2.4.57: The wind chill factor represents the equivalent air temperature at ...
 2.4.58: Redo 57(a) (d) for an air temperature of 10 C.
 2.4.59: In 2011 the U.S. Postal Service charged $0.88 postage for firstcla...
 2.4.60: Graph y = x2 . Then on the same screen graph y = x2 + 2, followed b...
 2.4.61: Graph y = x2 . Then on the same screen graph y = 1x  222 , followe...
 2.4.62: Graph y = 0 x 0 . Then on the same screen graph y = 2 0 x 0 , follo...
 2.4.63: Graph y = x2 . Then on the same screen graph y = x2 . What pattern...
 2.4.64: Graph y = 1x. Then on the same screen graph y = 1 x. What pattern ...
 2.4.65: Graph y = x3 . Then on the same screen graph y = 1x  123 + 2. Coul...
 2.4.66: Graph y = x2 , y = x4 , and y = x6 on the same screen. What do you ...
 2.4.67: Graph y = x3 , y = x5 , and y = x7 on the same screen. What do you ...
 2.4.68: Consider the equation y = b 1 if x is rational 0 if x is irrational...
 2.4.69: Consider the equation y = b 1 if x is rational 0 if x is irrational...
Solutions for Chapter 2.4: Library of Functions; Piecewisedefined Functions
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 2.4: Library of Functions; Piecewisedefined Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Since 69 problems in chapter 2.4: Library of Functions; Piecewisedefined Functions have been answered, more than 59765 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.4: Library of Functions; Piecewisedefined Functions includes 69 full stepbystep solutions. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

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.

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

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.

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.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

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

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

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

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.

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

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

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.

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

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·