 Chapter 4.3: In 14, determine whether the function is a polynomial function, rat...
 Chapter 4.4: In 14, determine whether the function is a polynomial function, rat...
 Chapter 4.5: In 57, graph each function using transformations (shifting, compres...
 Chapter 4.6: In 57, graph each function using transformations (shifting, compres...
 Chapter 4.7: In 57, graph each function using transformations (shifting, compres...
 Chapter 4.8: In 811, analyze each polynomial function by following Steps 1 throu...
 Chapter 4.9: In 811, analyze each polynomial function by following Steps 1 throu...
 Chapter 4.10: In 811, analyze each polynomial function by following Steps 1 throu...
 Chapter 4.11: In 811, analyze each polynomial function by following Steps 1 throu...
 Chapter 4.12: In 12 and 13, find the remainder R when f1x2 is divided by g1x2. Is...
 Chapter 4.13: In 12 and 13, find the remainder R when f1x2 is divided by g1x2. Is...
 Chapter 4.14: Find the value of f1x2 = 12x6  8x4 + 1 at x = 4.
 Chapter 4.15: List all the potential rational zeros of f1x2 = 12x8  x7 + 6x4  x...
 Chapter 4.16: In 16 18, use the Rational Zeros Theorem to find all the real zeros...
 Chapter 4.17: In 16 18, use the Rational Zeros Theorem to find all the real zeros...
 Chapter 4.18: In 16 18, use the Rational Zeros Theorem to find all the real zeros...
 Chapter 4.19: In 19 and 20, solve each equation in the real number system.
 Chapter 4.20: In 19 and 20, solve each equation in the real number system.
 Chapter 4.21: In 21 and 22, find bounds to the real zeros of each polynomial func...
 Chapter 4.22: In 21 and 22, find bounds to the real zeros of each polynomial func...
 Chapter 4.23: In 23 and 24, use the Intermediate Value Theorem to show that each ...
 Chapter 4.24: In 23 and 24, use the Intermediate Value Theorem to show that each ...
 Chapter 4.25: In 25 and 26, information is given about a complex polynomial funct...
 Chapter 4.26: In 25 and 26, information is given about a complex polynomial funct...
 Chapter 4.27: In 2730, find the complex zeros of each polynomial function f1x). W...
 Chapter 4.28: In 2730, find the complex zeros of each polynomial function f1x). W...
 Chapter 4.29: In 2730, find the complex zeros of each polynomial function f1x). W...
 Chapter 4.30: In 2730, find the complex zeros of each polynomial function f1x). W...
 Chapter 4.31: In 31 and 32, find the domain of each rational function. Find any h...
 Chapter 4.32: In 31 and 32, find the domain of each rational function. Find any h...
 Chapter 4.33: In 3338, discuss each rational function following Steps 17 given on...
 Chapter 4.34: In 3338, discuss each rational function following Steps 17 given on...
 Chapter 4.35: In 3338, discuss each rational function following Steps 17 given on...
 Chapter 4.36: In 3338, discuss each rational function following Steps 17 given on...
 Chapter 4.37: In 3338, discuss each rational function following Steps 17 given on...
 Chapter 4.38: In 3338, discuss each rational function following Steps 17 given on...
 Chapter 4.39: Use the graph below of a polynomial function y = f1x2 to solve (a) ...
 Chapter 4.40: Use the graph below of a rational function y = R1x2 to (a) identify...
 Chapter 4.41: In 4145, solve each inequality. Graph the solution set
 Chapter 4.42: In 4145, solve each inequality. Graph the solution set
 Chapter 4.43: In 4145, solve each inequality. Graph the solution set
 Chapter 4.44: In 4145, solve each inequality. Graph the solution set
 Chapter 4.45: In 4145, solve each inequality. Graph the solution set
 Chapter 4.46: A can in the shape of a right circular cylinder is required to have...
 Chapter 4.47: The following data represent the percentage of persons in the Unite...
 Chapter 4.48: Design a polynomial function with the following characteristics: de...
 Chapter 4.49: Design a rational function with the following characteristics: thre...
 Chapter 4.50: The illustration shows the graph of a polynomial function. (a) Is t...
Solutions for Chapter Chapter 4: Polynomial and Rational Functions
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter Chapter 4: Polynomial and Rational Functions
Get Full SolutionsPrecalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. Chapter Chapter 4: Polynomial and Rational Functions includes 48 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 48 problems in chapter Chapter 4: Polynomial and Rational Functions have been answered, more than 55790 students have viewed full stepbystep solutions from this chapter. 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.

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.)

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).

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

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.

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

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Iterative method.
A sequence of steps intended to approach the desired solution.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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).

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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.