 2.2.1: The intercepts of the equation x2 + 4y2 = 16 are __________________...
 2.2.2: The point (2, 6) is on the graph of the equation x = 2y  2. (p. ...
 2.2.3: A set of points in the xyplane is the graph of a function if and o...
 2.2.4: If the point (5, 3) is a point on the graph of f, then f( ) = ____...
 2.2.5: Find a so that the point (1, 2) is on the graph of f1x2 = ax2 + 4.
 2.2.6: A function can have more than one yintercept.
 2.2.7: The graph of a function y = f1x2 always crosses the yaxis
 2.2.8: The yintercept of the graph of the function y = f1x2, whose domain...
 2.2.9: (a) Find f102 and f1 62. (b) Find f162 and f1112. (c) Is f132 posi...
 2.2.10: Use the given graph of the function f to answer parts (a) (n). (a) ...
 2.2.11: In 1122, determine whether the graph is that of a function by using...
 2.2.12: In 1122, determine whether the graph is that of a function by using...
 2.2.13: In 1122, determine whether the graph is that of a function by using...
 2.2.14: In 1122, determine whether the graph is that of a function by using...
 2.2.15: In 1122, determine whether the graph is that of a function by using...
 2.2.16: In 1122, determine whether the graph is that of a function by using...
 2.2.17: In 1122, determine whether the graph is that of a function by using...
 2.2.18: In 1122, determine whether the graph is that of a function by using...
 2.2.19: In 1122, determine whether the graph is that of a function by using...
 2.2.20: In 1122, determine whether the graph is that of a function by using...
 2.2.21: In 1122, determine whether the graph is that of a function by using...
 2.2.22: In 1122, determine whether the graph is that of a function by using...
 2.2.23: In 2328, answer the questions about the given function.
 2.2.24: In 2328, answer the questions about the given function.
 2.2.25: In 2328, answer the questions about the given function.
 2.2.26: In 2328, answer the questions about the given function.
 2.2.27: In 2328, answer the questions about the given function.
 2.2.28: In 2328, answer the questions about the given function.
 2.2.29: According to physicist Peter Brancazio, the key to a successful fou...
 2.2.30: The last player in the NBA to use an underhand foul shot (a granny ...
 2.2.31: A golf ball is hit with an initial velocity of 130 feet per second ...
 2.2.32: The crosssectional area of a beam cut from a log with radius 1 foo...
 2.2.33: If an object weighs m pounds at sea level, then its weight W (in po...
 2.2.34: If an object weighs m pounds at sea level, then its weight W (in po...
 2.2.35: The graph of two functions, f and g, is illustrated. Use the graph ...
 2.2.36: Let C be the function whose graph is given in the next column. This...
 2.2.37: Let C be the function whose graph is given below. This graph repres...
 2.2.38: Describe how you would proceed to find the domain and range of a fu...
 2.2.39: How many xintercepts can the graph of a function have? How many y...
 2.2.40: Is a graph that consists of a single point the graph of a function?...
 2.2.41: Match each of the following functions with the graph on the next pa...
 2.2.42: Match each of the following functions with the graph that best desc...
 2.2.43: Consider the following scenario: Barbara decides to take a walk. Sh...
 2.2.44: Consider the following scenario: Jayne enjoys riding her bicycle th...
 2.2.45: The following sketch represents the distance d (in miles) that Kevi...
 2.2.46: The following sketch represents the speed v (in miles per hour) of ...
 2.2.47: Draw the graph of a function whose domain is 5x 3 x 8, x 56 and wh...
 2.2.48: Is there a function whose graph is symmetric with respect to the x...
Solutions for Chapter 2.2: The Graph of a Function
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 2.2: The Graph of a Function
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.2: The Graph of a Function includes 48 full stepbystep solutions. Since 48 problems in chapter 2.2: The Graph of a Function have been answered, more than 59540 students have viewed full stepbystep solutions from this chapter. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6.

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.

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

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 IIĀ· Condition numbers measure the sensitivity of the output to change in the input.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

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

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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

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.

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

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.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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

Solvable system Ax = b.
The right side b is in the column space of A.

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).