 4.1.1: The intercepts of the equation 9x2 + 4y = 36 are __________________...
 4.1.2: Is the expression 4x3  3.6x2  22 a polynomial? If so, what is its...
 4.1.3: To graph y = x2  4, you would shift the graph of y = x2 ________ a...
 4.1.4: Use a graphing utility to approximate (rounded to two decimal place...
 4.1.5: The xintercepts of the graph of a function y = f1x2 are the real s...
 4.1.6: If g(5) = 0, what point is on the graph of g? What is the correspon...
 4.1.7: The graph of every polynomial function is both _________ and ______...
 4.1.8: If r is a real zero of even multiplicity of a function f, then the ...
 4.1.9: The graphs of power functions of the form f1x2 = xn, where n 2 is a...
 4.1.10: If r is a solution to the equation f1x2 = 0, name three additional ...
 4.1.11: The points at which a graph changes direction (from increasing to d...
 4.1.12: The graph of the function f1x2 = 3x4  x3 + 5x2  2x  7 will behav...
 4.1.13: If f1x2 = 2x5 + x3  5x2 + 7, then lim xS f1x2 = ________ and lim...
 4.1.14: Explain what the notation lim xS f1x2 =  means.
 4.1.15: In 1526, determine which functions are polynomial functions. For th...
 4.1.16: In 1526, determine which functions are polynomial functions. For th...
 4.1.17: In 1526, determine which functions are polynomial functions. For th...
 4.1.18: In 1526, determine which functions are polynomial functions. For th...
 4.1.19: In 1526, determine which functions are polynomial functions. For th...
 4.1.20: In 1526, determine which functions are polynomial functions. For th...
 4.1.21: In 1526, determine which functions are polynomial functions. For th...
 4.1.22: In 1526, determine which functions are polynomial functions. For th...
 4.1.23: In 1526, determine which functions are polynomial functions. For th...
 4.1.24: In 1526, determine which functions are polynomial functions. For th...
 4.1.25: In 1526, determine which functions are polynomial functions. For th...
 4.1.26: In 1526, determine which functions are polynomial functions. For th...
 4.1.27: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.28: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.29: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.30: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.31: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.32: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.33: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.34: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.35: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.36: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.37: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.38: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.39: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.40: In 27 40, use transformations of the graph of y = x4 or y = x5 to g...
 4.1.41: In 41 48, form a polynomial function whose real zeros and degree ar...
 4.1.42: In 41 48, form a polynomial function whose real zeros and degree ar...
 4.1.43: In 41 48, form a polynomial function whose real zeros and degree ar...
 4.1.44: In 41 48, form a polynomial function whose real zeros and degree ar...
 4.1.45: In 41 48, form a polynomial function whose real zeros and degree ar...
 4.1.46: In 41 48, form a polynomial function whose real zeros and degree ar...
 4.1.56: In 49 60, for each polynomial function: (a) List each real zero and...
 4.1.57: In 49 60, for each polynomial function: (a) List each real zero and...
 4.1.58: In 49 60, for each polynomial function: (a) List each real zero and...
 4.1.59: In 49 60, for each polynomial function: (a) List each real zero and...
 4.1.60: In 49 60, for each polynomial function: (a) List each real zero and...
 4.1.61: In 6164, identify which of the graphs could be the graph of a polyn...
 4.1.62: In 6164, identify which of the graphs could be the graph of a polyn...
 4.1.63: In 6164, identify which of the graphs could be the graph of a polyn...
 4.1.64: In 6164, identify which of the graphs could be the graph of a polyn...
 4.1.65: In 6568, construct a polynomial function that might have the given ...
 4.1.66: In 6568, construct a polynomial function that might have the given ...
 4.1.67: In 6568, construct a polynomial function that might have the given ...
 4.1.68: In 6568, construct a polynomial function that might have the given ...
 4.1.69: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.70: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.71: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.72: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.73: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.74: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.75: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.76: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.77: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.78: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.79: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.80: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.81: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.82: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.83: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.84: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.85: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.86: In 69 86, analyze each polynomial function by following Steps 1 thr...
 4.1.87: In 8794, analyze each polynomial function f by following Steps 1 th...
 4.1.88: In 8794, analyze each polynomial function f by following Steps 1 th...
 4.1.89: In 8794, analyze each polynomial function f by following Steps 1 th...
 4.1.90: In 8794, analyze each polynomial function f by following Steps 1 th...
 4.1.91: In 8794, analyze each polynomial function f by following Steps 1 th...
 4.1.92: In 8794, analyze each polynomial function f by following Steps 1 th...
 4.1.93: In 8794, analyze each polynomial function f by following Steps 1 th...
 4.1.94: In 8794, analyze each polynomial function f by following Steps 1 th...
 4.1.95: In 95102, analyze each polynomial function by following Steps 1 thr...
 4.1.96: In 95102, analyze each polynomial function by following Steps 1 thr...
 4.1.97: In 95102, analyze each polynomial function by following Steps 1 thr...
 4.1.98: In 95102, analyze each polynomial function by following Steps 1 thr...
 4.1.99: In 95102, analyze each polynomial function by following Steps 1 thr...
 4.1.100: In 95102, analyze each polynomial function by following Steps 1 thr...
 4.1.101: In 95102, analyze each polynomial function by following Steps 1 thr...
 4.1.102: In 95102, analyze each polynomial function by following Steps 1 thr...
 4.1.103: Zeros: 3, 1, 4; degree 3; yintercept: 36
 4.1.104: Zeros: 4, 1, 2; degree 3; yintercept: 16
 4.1.105: Zeros: 5 (multiplicity 2); 2 (multiplicity 1); 4 (multiplicity 1);...
 4.1.106: Zeros: 4 (multiplicity 1); 0 (multiplicity 3); 2 (multiplicity 1);...
 4.1.107: G1x2 = 1x + 322 1x  22 (a) Identify the xintercepts of the graph ...
 4.1.108: h1x2 = 1x + 22 1x  423 (a) Identify the xintercepts of the graph ...
 4.1.109: In 2005, Hurricane Katrina struck the Gulf Coast of the United Stat...
 4.1.110: The following data represent the cost C (in thousands of dollars) o...
 4.1.111: The following data represent the temperature T (Fahrenheit) in Kans...
 4.1.112: Suppose that you make deposits of $500 at the beginning of every ye...
 4.1.113: In calculus, you will learn that certain functions can be approxima...
 4.1.114: Can the graph of a polynomial function have no yintercept? Can it ...
 4.1.115: Write a few paragraphs that provide a general strategy for graphing...
 4.1.116: Make up a polynomial function that has the following characteristic...
 4.1.117: Make up two polynomial functions, not of the same degree, with the ...
 4.1.118: The graph of a polynomial function is always smooth and continuous....
 4.1.119: Which of the following statements are true regarding the graph of t...
 4.1.120: The illustration shows the graph of a polynomial function. x y (a) ...
 4.1.121: Design a polynomial function with the following characteristics: de...
 4.1.122: Grab the slider for the exponent a and move it from 1 to 2 to 3. Wh...
 4.1.123: On the same graph, grab the slider for the exponent a and move it t...
 4.1.124: On the same graph, grab the slider for the exponent b and move it t...
 4.1.125: Experiment with the graph by adjusting a, b, and c. Based on your e...
 4.1.126: Obtain a graph of the function for the various values of a, b, and ...
Solutions for Chapter 4.1: Polynomial Functions and Models
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 4.1: Polynomial Functions and Models
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.1: Polynomial Functions and Models includes 117 full stepbystep solutions. Since 117 problems in chapter 4.1: Polynomial Functions and Models have been answered, more than 55881 students have viewed full stepbystep solutions from this chapter. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

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).

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

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

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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

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

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

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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.