 3.5.1: When examining the formula of a function that is the result of mult...
 3.5.2: When examining the formula of a function that is the result of mult...
 3.5.3: When examining the formula of a function that is the result of mult...
 3.5.4: When examining the formula of a function that is the result of mult...
 3.5.5: How can you determine whether a function is odd or even from the fo...
 3.5.6: For the following exercises, write a formula for the function obtai...
 3.5.7: For the following exercises, write a formula for the function obtai...
 3.5.8: For the following exercises, write a formula for the function obtai...
 3.5.9: For the following exercises, write a formula for the function obtai...
 3.5.10: For the following exercises, describe how the graph of the function...
 3.5.11: For the following exercises, describe how the graph of the function...
 3.5.12: For the following exercises, describe how the graph of the function...
 3.5.13: For the following exercises, describe how the graph of the function...
 3.5.14: For the following exercises, describe how the graph of the function...
 3.5.15: For the following exercises, describe how the graph of the function...
 3.5.16: For the following exercises, describe how the graph of the function...
 3.5.17: For the following exercises, describe how the graph of the function...
 3.5.18: For the following exercises, describe how the graph of the function...
 3.5.19: For the following exercises, describe how the graph of the function...
 3.5.20: For the following exercises, determine the interval(s) on which the...
 3.5.21: For the following exercises, determine the interval(s) on which the...
 3.5.22: For the following exercises, determine the interval(s) on which the...
 3.5.23: For the following exercises, determine the interval(s) on which the...
 3.5.24: For the following exercises, use the graph of f(x) = 2x shown in Fi...
 3.5.25: For the following exercises, use the graph of f(x) = 2x shown in Fi...
 3.5.26: For the following exercises, use the graph of f(x) = 2x shown in Fi...
 3.5.27: For the following exercises, sketch a graph of the function as a tr...
 3.5.28: For the following exercises, sketch a graph of the function as a tr...
 3.5.29: For the following exercises, sketch a graph of the function as a tr...
 3.5.30: For the following exercises, sketch a graph of the function as a tr...
 3.5.31: Tabular representations for the functions f, g, and h are given bel...
 3.5.32: Tabular representations for the functions f, g, and h are given bel...
 3.5.33: For the following exercises, write an equation for each graphed fun...
 3.5.34: For the following exercises, write an equation for each graphed fun...
 3.5.35: For the following exercises, write an equation for each graphed fun...
 3.5.36: For the following exercises, write an equation for each graphed fun...
 3.5.37: For the following exercises, write an equation for each graphed fun...
 3.5.38: For the following exercises, write an equation for each graphed fun...
 3.5.39: For the following exercises, write an equation for each graphed fun...
 3.5.40: For the following exercises, write an equation for each graphed fun...
 3.5.41: For the following exercises, use the graphs of transformations of t...
 3.5.42: For the following exercises, use the graphs of transformations of t...
 3.5.43: For the following exercises, use the graphs of the transformed tool...
 3.5.44: For the following exercises, use the graphs of the transformed tool...
 3.5.45: For the following exercises, use the graphs of the transformed tool...
 3.5.46: For the following exercises, use the graphs of the transformed tool...
 3.5.47: For the following exercises, determine whether the function is odd,...
 3.5.48: For the following exercises, determine whether the function is odd,...
 3.5.49: For the following exercises, determine whether the function is odd,...
 3.5.50: For the following exercises, determine whether the function is odd,...
 3.5.51: For the following exercises, determine whether the function is odd,...
 3.5.52: For the following exercises, determine whether the function is odd,...
 3.5.53: For the following exercises, describe how the graph of each functio...
 3.5.54: For the following exercises, describe how the graph of each functio...
 3.5.55: For the following exercises, describe how the graph of each functio...
 3.5.56: For the following exercises, describe how the graph of each functio...
 3.5.57: For the following exercises, describe how the graph of each functio...
 3.5.58: For the following exercises, describe how the graph of each functio...
 3.5.59: For the following exercises, describe how the graph of each functio...
 3.5.60: For the following exercises, describe how the graph of each functio...
 3.5.61: For the following exercises, describe how the graph of each functio...
 3.5.62: For the following exercises, describe how the graph of each functio...
 3.5.63: For the following exercises, write a formula for the function g tha...
 3.5.64: For the following exercises, write a formula for the function g tha...
 3.5.65: For the following exercises, write a formula for the function g tha...
 3.5.66: For the following exercises, write a formula for the function g tha...
 3.5.67: For the following exercises, write a formula for the function g tha...
 3.5.68: For the following exercises, write a formula for the function g tha...
 3.5.69: For the following exercises, describe how the formula is a transfor...
 3.5.70: For the following exercises, describe how the formula is a transfor...
 3.5.71: For the following exercises, describe how the formula is a transfor...
 3.5.72: For the following exercises, describe how the formula is a transfor...
 3.5.73: For the following exercises, describe how the formula is a transfor...
 3.5.74: For the following exercises, describe how the formula is a transfor...
 3.5.75: For the following exercises, describe how the formula is a transfor...
 3.5.76: For the following exercises, describe how the formula is a transfor...
 3.5.77: For the following exercises, describe how the formula is a transfor...
 3.5.78: For the following exercises, use the graph in Figure 32 to sketch t...
 3.5.79: For the following exercises, use the graph in Figure 32 to sketch t...
 3.5.80: For the following exercises, use the graph in Figure 32 to sketch t...
 3.5.81: For the following exercises, use the graph in Figure 32 to sketch t...
Solutions for Chapter 3.5: TRANSFORMATION OF FUNCTIONS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 3.5: TRANSFORMATION OF FUNCTIONS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781938168383. This textbook survival guide was created for the textbook: College Algebra, edition: 1. Chapter 3.5: TRANSFORMATION OF FUNCTIONS includes 81 full stepbystep solutions. Since 81 problems in chapter 3.5: TRANSFORMATION OF FUNCTIONS have been answered, more than 30178 students have viewed full stepbystep solutions from this chapter.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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).

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.

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

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

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.

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

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.

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

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

Outer product uv T
= column times row = rank one matrix.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

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

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

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.