 4.1: Determine whether the statement is true or false.If f 1x2 = 1x + a2...
 4.2: Determine whether the statement is true or false.The graph of a rat...
 4.3: Determine whether the statement is true or false.For the function g...
 4.4: Determine whether the statement is true or false.The graph of P1x2 ...
 4.5: Determine whether the statement is true or false.The domain of the ...
 4.6: Use a graphing calculator to graph the polynomial function. Then es...
 4.7: Use a graphing calculator to graph the polynomial function. Then es...
 4.8: Use a graphing calculator to graph the polynomial function. Then es...
 4.9: Determine the leading term, the leading coefficient, and the degree...
 4.10: Determine the leading term, the leading coefficient, and the degree...
 4.11: Determine the leading term, the leading coefficient, and the degree...
 4.12: Determine the leading term, the leading coefficient, and the degree...
 4.13: Use the leadingterm test to describe the end behavior of the graph...
 4.14: Use the leadingterm test to describe the end behavior of the graph...
 4.15: Find the zeros of the polynomial function and state the multiplicit...
 4.16: Find the zeros of the polynomial function and state the multiplicit...
 4.17: Find the zeros of the polynomial function and state the multiplicit...
 4.18: Interest Compounded Annually. When P dollars is invested at interes...
 4.19: Cholesterol Level and the Risk of Heart Attack. The table below lis...
 4.20: Sketch the graph of the polynomial function.f 1x2 = x4 + 2x3 [4.2]
 4.21: Sketch the graph of the polynomial function.g1x2 = 1x  1231x + 222...
 4.22: Sketch the graph of the polynomial function.h1x2 = x3 + 3x2  x  3...
 4.23: Sketch the graph of the polynomial function.f 1x2 = x4  5x3 + 6x2 ...
 4.24: Sketch the graph of the polynomial function.g1x2 = 2x3 + 7x2  14x ...
 4.25: Using the intermediate value theorem, determine, if possible, wheth...
 4.26: Using the intermediate value theorem, determine, if possible, wheth...
 4.27: In each of the following, a polynomial P1x2 and a divisor d1x2 are ...
 4.28: In each of the following, a polynomial P1x2 and a divisor d1x2 are ...
 4.29: Use synthetic division to find the quotient and the remainder. [4.3...
 4.30: Use synthetic division to find the quotient and the remainder. [4.3...
 4.31: Use synthetic division to find the quotient and the remainder. [4.3...
 4.32: Use synthetic division to find the indicated function value. [4.3]f...
 4.33: Use synthetic division to find the indicated function value. [4.3]f...
 4.34: Use synthetic division to find the indicated function value. [4.3]f...
 4.35: Using synthetic division, determine whether the given numbers are z...
 4.36: Using synthetic division, determine whether the given numbers are z...
 4.37: Using synthetic division, determine whether the given numbers are z...
 4.38: Using synthetic division, determine whether the given numbers are z...
 4.39: Factor the polynomial f 1x2. Then solve the equation f 1x2 = 0. [4....
 4.40: Factor the polynomial f 1x2. Then solve the equation f 1x2 = 0. [4....
 4.41: Factor the polynomial f 1x2. Then solve the equation f 1x2 = 0. [4....
 4.42: Factor the polynomial f 1x2. Then solve the equation f 1x2 = 0. [4....
 4.43: Find a polynomial function of degree 3 with the given numbers as ze...
 4.44: Find a polynomial function of degree 3 with the given numbers as ze...
 4.45: Find a polynomial function of degree 3 with the given numbers as ze...
 4.46: Find a polynomial function of degree 4 with 5 as a zero of multipl...
 4.47: Find a polynomial function of degree 5 with 3 as a zero of multipl...
 4.48: Suppose that a polynomial function of degree 5 with rational coeffi...
 4.49: Suppose that a polynomial function of degree 5 with rational coeffi...
 4.50: Suppose that a polynomial function of degree 5 with rational coeffi...
 4.51: Find a polynomial function of lowest degree with rational coefficie...
 4.52: Find a polynomial function of lowest degree with rational coefficie...
 4.53: Find a polynomial function of lowest degree with rational coefficie...
 4.54: Find a polynomial function of lowest degree with rational coefficie...
 4.55: Find a polynomial function of lowest degree with rational coefficie...
 4.56: List all possible rational zeros. [4.4]h1x2 = 4x5  2x3 + 6x  12
 4.57: List all possible rational zeros. [4.4]g1x2 = 3x4  x3 + 5x2  x + 1
 4.58: List all possible rational zeros. [4.4]f 1x2 = x3  2x2 + x  24
 4.59: For each polynomial function: a) Find the rational zeros and then t...
 4.60: For each polynomial function: a) Find the rational zeros and then t...
 4.61: For each polynomial function: a) Find the rational zeros and then t...
 4.62: For each polynomial function: a) Find the rational zeros and then t...
 4.63: For each polynomial function: a) Find the rational zeros and then t...
 4.64: For each polynomial function: a) Find the rational zeros and then t...
 4.65: For each polynomial function: a) Find the rational zeros and then t...
 4.66: For each polynomial function: a) Find the rational zeros and then t...
 4.67: What does Descartes rule of signs tell you about the number of posi...
 4.68: What does Descartes rule of signs tell you about the number of posi...
 4.69: What does Descartes rule of signs tell you about the number of posi...
 4.70: Graph the function. Be sure to label all the asymptotes. List the d...
 4.71: Graph the function. Be sure to label all the asymptotes. List the d...
 4.72: Graph the function. Be sure to label all the asymptotes. List the d...
 4.73: Graph the function. Be sure to label all the asymptotes. List the d...
 4.74: In Exercises 74 and 75, find a rational function that satisfies the...
 4.75: In Exercises 74 and 75, find a rational function that satisfies the...
 4.76: Medical Dosage. The function N1t2 = 0.7t + 2000 8t + 9 , t 5, gives...
 4.77: Solve. [4.6]x2  9 6 0
 4.78: Solve. [4.6]2x2 7 3x + 2
 4.79: Solve. [4.6] 11  x21x + 421x  22 0
 4.80: Solve. [4.6]x  2x + 36 4
 4.81: Height of a Rocket. The function S1t2 = 16t 2 + 80t + 224 gives th...
 4.82: Population Growth. The population P, in thousands, of Novi is given...
 4.83: Determine the domain of the function g1x2 = x2 + 2x  3 x2  5x + 6...
 4.84: Determine the vertical asymptotes of the function f 1x2 = x  4 1x ...
 4.85: The graph of f 1x2 =  1 2 x4 + x3 + 1 is which of the following? [...
 4.86: Solvex2 5  2x [4.6] 87. ` 1  1x2 ` 6 3 [4.6]
 4.87: Solvex4  2x3 + 3x2  2x + 2 = 0 [4.4], [4.5]
 4.88: Solve1x  223 6 0 [4.6]
 4.89: Solve1x  223 6 0 [4.6]
 4.90: Express x3  1 as a product of linear factors. [4.4]
 4.91: Find k such that x + 3 is a factor of x3 + kx2 + kx  15. [4.3]
 4.92: When x2  4x + 3k is divided by x + 5, the remainder is 33. Find th...
 4.93: Find the domain of the function. [4.6]f 1x2 = 2x2 + 3x  10
 4.94: Find the domain of the function. [4.6]f 1x2 = 2x2  3.1x + 2.2 + 1.75
 4.95: Find the domain of the function. [4.6] 1x2 = 125  7x + 2
 4.96: Explain the difference between a polynomial function and a rational...
 4.97: Is it possible for a thirddegree polynomial with rational coeffici...
 4.98: Explain and contrast the three types of asymptotes considered for r...
 4.99: If P1x2 is an even function, and by Descartes rule of signs, P1x2 h...
 4.100: Explain why the graph of a rational function cannot have both a hor...
 4.101: Under what circumstances would a quadratic inequality have a soluti...
Solutions for Chapter 4: Polynomial Functions and Rational Functions
Full solutions for College Algebra: Graphs and Models  5th Edition
ISBN: 9780321783950
Solutions for Chapter 4: Polynomial Functions and Rational Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra: Graphs and Models, edition: 5. Chapter 4: Polynomial Functions and Rational Functions includes 101 full stepbystep solutions. Since 101 problems in chapter 4: Polynomial Functions and Rational Functions have been answered, more than 27446 students have viewed full stepbystep solutions from this chapter. College Algebra: Graphs and Models was written by and is associated to the ISBN: 9780321783950. This expansive textbook survival guide covers the following chapters and their solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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

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.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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

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.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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

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·

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