 3.2.1: The intercepts of the equation arex2 + 4y2 = 16
 3.2.2: True or False The point is on the graph of the equation12, 62 x =...
 3.2.3: A set of points in the xyplane is the graph of a function if and o...
 3.2.4: If the point is a point on the graph of then2 = . 15, 32
 3.2.5: Find a so that the point is on the graph of f1x2 = ax2 + 4. 11, 22
 3.2.6: True or False A function can have more than one yintercept.
 3.2.7: True or False The graph of a function always crosses the yaxisy = ...
 3.2.8: True or False The yintercept of the graph of the function y = f1x2...
 3.2.9: Use the given graph of the function f to answer parts(a)(n)(a) Find...
 3.2.10: Use the given graph of the function f to answer parts(a)(n).(a) Fin...
 3.2.11: In 1122, determine whether the graph is that of a function by using...
 3.2.12: In 1122, determine whether the graph is that of a function by using...
 3.2.13: In 1122, determine whether the graph is that of a function by using...
 3.2.14: In 1122, determine whether the graph is that of a function by using...
 3.2.15: In 1122, determine whether the graph is that of a function by using...
 3.2.16: In 1122, determine whether the graph is that of a function by using...
 3.2.17: In 1122, determine whether the graph is that of a function by using...
 3.2.18: In 1122, determine whether the graph is that of a function by using...
 3.2.19: In 1122, determine whether the graph is that of a function by using...
 3.2.20: In 1122, determine whether the graph is that of a function by using...
 3.2.21: In 1122, determine whether the graph is that of a function by using...
 3.2.22: In 1122, determine whether the graph is that of a function by using...
 3.2.23: In 2328, answer the questions about the given function.Is the point...
 3.2.24: In 2328, answer the questions about the given function.Is the point...
 3.2.25: In 2328, answer the questions about the given function.Is the point...
 3.2.26: In 2328, answer the questions about the given function.f1x2 = x2 + ...
 3.2.27: In 2328, answer the questions about the given function.Is the point...
 3.2.28: In 2328, answer the questions about the given function.Is the point...
 3.2.29: Freethrow Shots According to physicist Peter Brancazio, the key to...
 3.2.30: Granny Shots The last player in the NBA to use an underhand foul sh...
 3.2.31: Motion of a Golf Ball A golf ball is hit with an initial velocity o...
 3.2.32: Crosssectional Area The crosssectional area of a beam cut from a ...
 3.2.33: Cost of TransAtlantic Travel A Boeing 747 crosses the Atlantic Oce...
 3.2.34: Effect of Elevation on Weight If an object weighs m pounds at sea l...
 3.2.35: The graph of two functions, f and g, is illustrated. Use the graph ...
 3.2.36: Describe how you would proceed to find the domain and range of a fu...
 3.2.37: How many xintercepts can the graph of a function have? How many y...
 3.2.38: Is a graph that consists of a single point the graph of a function?...
 3.2.39: Match each of the following functions with the graph that best desc...
 3.2.40: Match each of the following functions with the graph that best desc...
 3.2.41: Consider the following scenario: Barbara decides to take a walk. Sh...
 3.2.42: Consider the following scenario: Jayne enjoys riding her bicycle th...
 3.2.43: The following sketch represents the distance d (in miles) that Kevi...
 3.2.44: The following sketch represents the speed (in miles per hour) of Mi...
 3.2.45: Draw the graph of a function whose domain is and whose range is Wha...
 3.2.46: Is there a function whose graph is symmetric with respect to the x...
Solutions for Chapter 3.2: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 3.2
Get Full SolutionsChapter 3.2 includes 46 full stepbystep solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Since 46 problems in chapter 3.2 have been answered, more than 60416 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. This expansive textbook survival guide covers the following chapters and their solutions.

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!

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

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.

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.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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!).

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

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

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

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.