 6.2.1: What role does the horizontal asymptote of an exponential function ...
 6.2.2: What is the advantage of knowing how to recognize transformations o...
 6.2.3: The graph of f(x) = 3x is reflected about the yaxis and stretched ...
 6.2.4: The graph of f(x) = _ 1 2 x is reflected about the yaxis and compr...
 6.2.5: The graph of f(x) = 10x is reflected about the xaxis and shifted u...
 6.2.6: The graph of f(x) = (1.68)x is shifted right 3 units, stretched ver...
 6.2.7: The graph of f(x) = _ 1 2 _ 1 4 x 2 + 4 is shifted downward 4 units...
 6.2.8: For the following exercises, graph the function and its reflection ...
 6.2.9: For the following exercises, graph the function and its reflection ...
 6.2.10: For the following exercises, graph the function and its reflection ...
 6.2.11: For the following exercises, graph each set of functions on the sam...
 6.2.12: For the following exercises, graph each set of functions on the sam...
 6.2.13: For the following exercises, match each function with one of the gr...
 6.2.14: For the following exercises, match each function with one of the gr...
 6.2.15: For the following exercises, match each function with one of the gr...
 6.2.16: For the following exercises, match each function with one of the gr...
 6.2.17: For the following exercises, match each function with one of the gr...
 6.2.18: For the following exercises, match each function with one of the gr...
 6.2.19: For the following exercises, use the graphs shown in Figure 13. All...
 6.2.20: For the following exercises, use the graphs shown in Figure 13. All...
 6.2.21: For the following exercises, use the graphs shown in Figure 13. All...
 6.2.22: For the following exercises, use the graphs shown in Figure 13. All...
 6.2.23: For the following exercises, graph the function and its reflection ...
 6.2.24: For the following exercises, graph the function and its reflection ...
 6.2.25: For the following exercises, graph the function and its reflection ...
 6.2.26: For the following exercises, graph the transformation of f(x) = 2x ...
 6.2.27: For the following exercises, graph the transformation of f(x) = 2x ...
 6.2.28: For the following exercises, graph the transformation of f(x) = 2x ...
 6.2.29: For the following exercises, describe the end behavior of the graph...
 6.2.30: For the following exercises, describe the end behavior of the graph...
 6.2.31: For the following exercises, describe the end behavior of the graph...
 6.2.32: For the following exercises, start with the graph of f(x) = 4x . Th...
 6.2.33: For the following exercises, start with the graph of f(x) = 4x . Th...
 6.2.34: For the following exercises, start with the graph of f(x) = 4x . Th...
 6.2.35: For the following exercises, start with the graph of f(x) = 4x . Th...
 6.2.36: For the following exercises, start with the graph of f(x) = 4x . Th...
 6.2.37: For the following exercises, start with the graph of f(x) = 4x . Th...
 6.2.38: For the following exercises, each graph is a transformation of y = ...
 6.2.39: For the following exercises, each graph is a transformation of y = ...
 6.2.40: For the following exercises, each graph is a transformation of y = ...
 6.2.41: For the following exercises, each graph is a transformation of y = ...
 6.2.42: For the following exercises, each graph is a transformation of y = ...
 6.2.43: For the following exercises, evaluate the exponential functions for...
 6.2.44: For the following exercises, evaluate the exponential functions for...
 6.2.45: For the following exercises, evaluate the exponential functions for...
 6.2.46: For the following exercises, use a graphing calculator to approxima...
 6.2.47: For the following exercises, use a graphing calculator to approxima...
 6.2.48: For the following exercises, use a graphing calculator to approxima...
 6.2.49: For the following exercises, use a graphing calculator to approxima...
 6.2.50: For the following exercises, use a graphing calculator to approxima...
 6.2.51: Explore and discuss the graphs of f(x) = (b)x and g(x) = _ 1 b x . ...
 6.2.52: Prove the conjecture made in the previous exercise.
 6.2.53: Explore and discuss the graphs of f(x) = 4x , g(x) = 4x 2 , and h(x...
 6.2.54: Prove the conjecture made in the previous exercise.
Solutions for Chapter 6.2: GRAPHS OF EXPONENTIAL FUNCTIONS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 6.2: GRAPHS OF EXPONENTIAL FUNCTIONS
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra, edition: 1. Since 54 problems in chapter 6.2: GRAPHS OF EXPONENTIAL FUNCTIONS have been answered, more than 32032 students have viewed full stepbystep solutions from this chapter. Chapter 6.2: GRAPHS OF EXPONENTIAL FUNCTIONS includes 54 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781938168383.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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

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

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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.

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).

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.

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

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