 2.5.1: Fill in each blank so that the resulting statement is true.The grap...
 2.5.2: Fill in each blank so that the resulting statement is true.The grap...
 2.5.3: Fill in each blank so that the resulting statement is true.The grap...
 2.5.4: Fill in each blank so that the resulting statement is true.The grap...
 2.5.5: Fill in each blank so that the resulting statement is true.The grap...
 2.5.6: Fill in each blank so that the resulting statement is true.The grap...
 2.5.7: Fill in each blank so that the resulting statement is true.True or ...
 2.5.8: In Exercises 116, use the graph of y = f(x) to graph eachfunction g...
 2.5.9: In Exercises 116, use the graph of y = f(x) to graph eachfunction g...
 2.5.10: In Exercises 116, use the graph of y = f(x) to graph eachfunction g...
 2.5.11: In Exercises 116, use the graph of y = f(x) to graph eachfunction g...
 2.5.12: In Exercises 116, use the graph of y = f(x) to graph eachfunction g...
 2.5.13: In Exercises 116, use the graph of y = f(x) to graph eachfunction g...
 2.5.14: In Exercises 116, use the graph of y = f(x) to graph eachfunction g...
 2.5.15: In Exercises 116, use the graph of y = f(x) to graph eachfunction g...
 2.5.16: In Exercises 116, use the graph of y = f(x) to graph eachfunction g...
 2.5.17: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.18: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.19: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.20: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.21: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.22: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.23: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.24: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.25: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.26: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.27: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.28: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.29: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.30: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.31: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.32: In Exercises 1732, use the graph of y = f(x) to graph eachfunction ...
 2.5.33: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.34: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.35: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.36: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.37: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.38: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.39: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.40: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.41: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.42: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.43: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.44: In Exercises 3344, use the graph of y = f(x) to graph eachfunction ...
 2.5.45: In Exercises 4552, use the graph of y = f(x) to graph eachfunction ...
 2.5.46: In Exercises 4552, use the graph of y = f(x) to graph eachfunction ...
 2.5.47: In Exercises 4552, use the graph of y = f(x) to graph eachfunction ...
 2.5.48: In Exercises 4552, use the graph of y = f(x) to graph eachfunction ...
 2.5.49: In Exercises 4552, use the graph of y = f(x) to graph eachfunction ...
 2.5.50: In Exercises 4552, use the graph of y = f(x) to graph eachfunction ...
 2.5.51: In Exercises 4552, use the graph of y = f(x) to graph eachfunction ...
 2.5.52: In Exercises 4552, use the graph of y = f(x) to graph eachfunction ...
 2.5.53: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.54: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.55: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.56: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.57: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.58: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.59: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.60: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.61: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.62: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.63: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.64: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.65: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.66: In Exercises 5366, begin by graphing the standard quadraticfunction...
 2.5.67: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.68: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.69: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.70: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.71: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.72: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.73: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.74: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.75: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.76: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.77: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.78: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.79: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.80: In Exercises 6780, begin by graphing the square root function,f(x) ...
 2.5.81: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.82: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.83: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.84: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.85: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.86: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.87: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.88: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.89: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.90: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.91: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.92: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.93: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.94: In Exercises 8194, begin by graphing the absolute value function,f(...
 2.5.95: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.96: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.97: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.98: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.99: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.100: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.101: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.102: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.103: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.104: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.105: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.106: In Exercises 95106, begin by graphing the standard cubicfunction, f...
 2.5.107: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.108: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.109: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.110: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.111: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.112: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.113: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.114: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.115: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.116: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.117: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.118: In Exercises 107118, begin by graphing the cube root function,f(x) ...
 2.5.119: In Exercises 119122, use transformations of the graph of thegreates...
 2.5.120: In Exercises 119122, use transformations of the graph of thegreates...
 2.5.121: In Exercises 119122, use transformations of the graph of thegreates...
 2.5.122: In Exercises 119122, use transformations of the graph of thegreates...
 2.5.123: In Exercises 123126, write a possible equation for the functionwhos...
 2.5.124: In Exercises 123126, write a possible equation for the functionwhos...
 2.5.125: In Exercises 123126, write a possible equation for the functionwhos...
 2.5.126: In Exercises 123126, write a possible equation for the functionwhos...
 2.5.127: The function f(x) = 2.91x + 20.1 models the medianheight, f(x), in ...
 2.5.128: The function f(x) = 3.11x + 19 models the median height,f(x), in in...
 2.5.129: What must be done to a functions equation so that its graphis shift...
 2.5.130: What must be done to a functions equation so that its graphis shift...
 2.5.131: What must be done to a functions equation so that its graphis refle...
 2.5.132: What must be done to a functions equation so that its graphis refle...
 2.5.133: What must be done to a functions equation so that its graphis stret...
 2.5.134: What must be done to a functions equation so that its graphis shrun...
 2.5.135: a. Use a graphing utility to graph f(x) = x2 + 1.b. Graph f(x) = x2...
 2.5.136: a. Use a graphing utility to graph f(x) = x2 + 1.b. Graph f(x) = x2...
 2.5.137: During the winter, you program your homethermostat so that at midni...
 2.5.138: During the winter, you program your homethermostat so that at midni...
 2.5.139: During the winter, you program your homethermostat so that at midni...
 2.5.140: During the winter, you program your homethermostat so that at midni...
 2.5.141: In Exercises 141144, determine whether each statement is trueor fal...
 2.5.142: In Exercises 141144, determine whether each statement is trueor fal...
 2.5.143: In Exercises 141144, determine whether each statement is trueor fal...
 2.5.144: In Exercises 141144, determine whether each statement is trueor fal...
 2.5.145: In Exercises 145148, functions f and g are graphed in the samerecta...
 2.5.146: In Exercises 145148, functions f and g are graphed in the samerecta...
 2.5.147: In Exercises 145148, functions f and g are graphed in the samerecta...
 2.5.148: In Exercises 145148, functions f and g are graphed in the samerecta...
 2.5.149: For Exercises 149152, assume that (a, b) is a point on the graphof ...
 2.5.150: For Exercises 149152, assume that (a, b) is a point on the graphof ...
 2.5.151: For Exercises 149152, assume that (a, b) is a point on the graphof ...
 2.5.152: For Exercises 149152, assume that (a, b) is a point on the graphof ...
 2.5.153: The length of a rectangle exceeds the width by 13 yards.If the peri...
 2.5.154: Solve: 2x + 10  4 = x.(Section 1.6, Example 3)
 2.5.155: Multiply and write the product in standard form:(3  7i)(5 + 2i).(S...
 2.5.156: Exercises 156158 will help you prepare for the material coveredin t...
 2.5.157: Exercises 156158 will help you prepare for the material coveredin t...
 2.5.158: Exercises 156158 will help you prepare for the material coveredin t...
Solutions for Chapter 2.5: Transformations of Functions
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 2.5: Transformations of Functions
Get Full SolutionsCollege Algebra was written by and is associated to the ISBN: 9780134469164. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.5: Transformations of Functions includes 158 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 7. Since 158 problems in chapter 2.5: Transformations of Functions have been answered, more than 29807 students have viewed full stepbystep solutions from this chapter.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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

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

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

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

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

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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.

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.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.