 5.1.1: The intercepts of the equation 9x2 + 4y = 36 are
 5.1.2: Is the expression 4x3  3.6x2  12 a polynomial? If so, what is its...
 5.1.3: To graph y = x2  4, you would shift the graph of y = x2 a distance...
 5.1.4: Use a graphing utility to approximate (rounded to two decimal place...
 5.1.5: True or False The xintercepts of the graph of a function y = f1x2 ...
 5.1.6: If g152 = 0, what point is on the graph of g? What is the correspon...
 5.1.7: The graph of every polynomial function is both and
 5.1.8: If r is a real zero of even multiplicity of a function f, then the ...
 5.1.9: The graphs of power functions of the form f1x2 = xn where n is an e...
 5.1.10: f r is a solution to the equation , name three additional statement...
 5.1.11: The points at which a graph changes direction (from increasing to d...
 5.1.12: The graph of the function f1x2 = 3x4  x3 + 5x2  2x  7 will behav...
 5.1.13: If then f1x2 = 2x f1x2 = 5 + x3  5x2 + 7 and limx:qf1x2 =
 5.1.14: Explain what the notation lim means. x:qf1x2 =  q means.
 5.1.15: In 1526, determine which functions are polynomial functions. For th...
 5.1.16: In 1526, determine which functions are polynomial functions. For th...
 5.1.17: In 1526, determine which functions are polynomial functions. For th...
 5.1.18: In 1526, determine which functions are polynomial functions. For th...
 5.1.19: In 1526, determine which functions are polynomial functions. For th...
 5.1.20: In 1526, determine which functions are polynomial functions. For th...
 5.1.21: In 1526, determine which functions are polynomial functions. For th...
 5.1.22: In 1526, determine which functions are polynomial functions. For th...
 5.1.23: In 1526, determine which functions are polynomial functions. For th...
 5.1.24: In 1526, determine which functions are polynomial functions. For th...
 5.1.25: In 1526, determine which functions are polynomial functions. For th...
 5.1.26: In 1526, determine which functions are polynomial functions. For th...
 5.1.27: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.28: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.29: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.30: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.31: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.32: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.33: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.34: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.35: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.36: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.37: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.38: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.39: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.40: In 2740, use transformations of the graph of y = x4 or y = x5 to gr...
 5.1.41: In 4148, form a polynomial function whose real zeros and degree are...
 5.1.42: In 4148, form a polynomial function whose real zeros and degree are...
 5.1.43: In 4148, form a polynomial function whose real zeros and degree are...
 5.1.44: In 4148, form a polynomial function whose real zeros and degree are...
 5.1.45: In 4148, form a polynomial function whose real zeros and degree are...
 5.1.46: In 4148, form a polynomial function whose real zeros and degree are...
 5.1.47: In 4148, form a polynomial function whose real zeros and degree are...
 5.1.48: In 4148, form a polynomial function whose real zeros and degree are...
 5.1.49: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.50: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.51: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.52: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.53: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.54: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.55: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.56: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.57: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.58: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.59: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.60: In 4960, for each polynomial function: (a) List each real zero and ...
 5.1.61: In 6164, identify which of the graphs could be the graph of a polyn...
 5.1.62: In 6164, identify which of the graphs could be the graph of a polyn...
 5.1.63: In 6164, identify which of the graphs could be the graph of a polyn...
 5.1.64: In 6164, identify which of the graphs could be the graph of a polyn...
 5.1.65: In 6568, construct a polynomial function that might have the given ...
 5.1.66: In 6568, construct a polynomial function that might have the given ...
 5.1.67: In 6568, construct a polynomial function that might have the given ...
 5.1.68: In 6568, construct a polynomial function that might have the given ...
 5.1.69: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.70: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.71: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.72: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.73: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.74: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.75: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.76: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.77: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.78: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.79: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.80: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.81: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.82: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.83: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.84: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.85: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.86: In 6986, analyze each polynomial function by following Steps 1 thro...
 5.1.87: In 8794, analyze each polynomial function f by following Steps 1 th...
 5.1.88: In 8794, analyze each polynomial function f by following Steps 1 th...
 5.1.89: In 8794, analyze each polynomial function f by following Steps 1 th...
 5.1.90: In 8794, analyze each polynomial function f by following Steps 1 th...
 5.1.91: In 8794, analyze each polynomial function f by following Steps 1 th...
 5.1.92: In 8794, analyze each polynomial function f by following Steps 1 th...
 5.1.93: In 8794, analyze each polynomial function f by following Steps 1 th...
 5.1.94: In 8794, analyze each polynomial function f by following Steps 1 th...
 5.1.95: In 95102, analyze each polynomial function by following Steps 1 thr...
 5.1.96: In 95102, analyze each polynomial function by following Steps 1 thr...
 5.1.97: In 95102, analyze each polynomial function by following Steps 1 thr...
 5.1.98: In 95102, analyze each polynomial function by following Steps 1 thr...
 5.1.99: In 95102, analyze each polynomial function by following Steps 1 thr...
 5.1.100: In 95102, analyze each polynomial function by following Steps 1 thr...
 5.1.101: In 95102, analyze each polynomial function by following Steps 1 thr...
 5.1.102: In 95102, analyze each polynomial function by following Steps 1 thr...
 5.1.103: In 103106, construct a polynomial function f with the given charact...
 5.1.104: In 103106, construct a polynomial function f with the given charact...
 5.1.105: In 103106, construct a polynomial function f with the given charact...
 5.1.106: In 103106, construct a polynomial function f with the given charact...
 5.1.107: G1x2 = 1x + 322 1x  22(a) Identify the xintercepts of the graph o...
 5.1.108: h1x2 = 1x + 221x  423(a) Identify the xintercepts of the graph of...
 5.1.109: Hurricanes In 2005, Hurricane Katrina struck the Gulf Coast of the ...
 5.1.110: Cost of Manufacturing The following data represent the cost C (in t...
 5.1.111: Temperature The following data represent the temperature T ( Fahren...
 5.1.112: Future Value of Money Suppose that you make deposits of $500 at the...
 5.1.113: A Geometric Series In calculus, you will learn that certain functio...
 5.1.114: Can the graph of a polynomial function have no yintercept? Can it ...
 5.1.115: Write a few paragraphs that provide a general strategy for graphing...
 5.1.116: Make up a polynomial that has the following characteristics: crosse...
 5.1.117: Make up two polynomials, not of the same degree, with the following...
 5.1.118: The graph of a polynomial function is always smooth and continuous....
 5.1.119: Which of the following statements are true regarding the graph of t...
 5.1.120: The illustration shows the graph of a polynomial function. x y (a) ...
 5.1.121: Design a polynomial function with the following characteristics: de...
Solutions for Chapter 5.1: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 5.1
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Since 121 problems in chapter 5.1 have been answered, more than 62117 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Chapter 5.1 includes 121 full stepbystep solutions.

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

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.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

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.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

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

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.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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).

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.

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

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

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

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

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·