 2.2.2.2.1: The graphs of all polynomial functions are _______ , which means th...
 2.2.2.2.2: The _______ is used to determine the lefthand and righthand behav...
 2.2.2.2.3: A polynomial function of degree has at most _______ real zeros and ...
 2.2.2.2.4: If is a zero of a polynomial function then the following statements...
 2.2.2.2.5: If a zero of a polynomial function is of even multiplicity, then th...
 2.2.2.2.6: If a zero of a polynomial function is of even multiplicity, then th...
 2.2.2.2.7: In Exercises 1 8, match the polynomial function with its graph. [Th...
 2.2.2.2.8: In Exercises 1 8, match the polynomial function with its graph. [Th...
 2.2.2.2.9: In Exercises 9 and 10, sketch the graph of and each specified trans...
 2.2.2.2.10: In Exercises 9 and 10, sketch the graph of and each specified trans...
 2.2.2.2.11: Graphical Analysis In Exercises 1114, use a graphing utility to gra...
 2.2.2.2.12: Graphical Analysis In Exercises 1114, use a graphing utility to gra...
 2.2.2.2.13: Graphical Analysis In Exercises 1114, use a graphing utility to gra...
 2.2.2.2.14: Graphical Analysis In Exercises 1114, use a graphing utility to gra...
 2.2.2.2.15: In Exercises 1522, use the Leading Coefficient Test to describe the...
 2.2.2.2.16: In Exercises 1522, use the Leading Coefficient Test to describe the...
 2.2.2.2.17: In Exercises 1522, use the Leading Coefficient Test to describe the...
 2.2.2.2.18: In Exercises 1522, use the Leading Coefficient Test to describe the...
 2.2.2.2.19: In Exercises 1522, use the Leading Coefficient Test to describe the...
 2.2.2.2.20: In Exercises 1522, use the Leading Coefficient Test to describe the...
 2.2.2.2.21: In Exercises 1522, use the Leading Coefficient Test to describe the...
 2.2.2.2.22: In Exercises 1522, use the Leading Coefficient Test to describe the...
 2.2.2.2.23: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.24: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.25: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.26: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.27: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.28: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.29: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.30: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.31: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.32: In Exercises 2332, find all the real zeros of the polynomial functi...
 2.2.2.2.33: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.34: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.35: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.36: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.37: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.38: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.39: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.40: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.41: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.42: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.43: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.44: Graphical Analysis In Exercises 3344, (a) find the zeros algebraica...
 2.2.2.2.45: In Exercises 4548, use a graphing utility to graph the function and...
 2.2.2.2.46: In Exercises 4548, use a graphing utility to graph the function and...
 2.2.2.2.47: In Exercises 4548, use a graphing utility to graph the function and...
 2.2.2.2.48: In Exercises 4548, use a graphing utility to graph the function and...
 2.2.2.2.49: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.50: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.51: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.52: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.53: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.54: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.55: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.56: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.57: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.58: In Exercises 4958, find a polynomial function that has the given ze...
 2.2.2.2.59: In Exercises 5964, find a polynomial function with the given zeros,...
 2.2.2.2.60: In Exercises 5964, find a polynomial function with the given zeros,...
 2.2.2.2.61: In Exercises 5964, find a polynomial function with the given zeros,...
 2.2.2.2.62: In Exercises 5964, find a polynomial function with the given zeros,...
 2.2.2.2.63: In Exercises 5964, find a polynomial function with the given zeros,...
 2.2.2.2.64: In Exercises 5964, find a polynomial function with the given zeros,...
 2.2.2.2.65: In Exercises 6568, sketch the graph of a polynomial function that s...
 2.2.2.2.66: In Exercises 6568, sketch the graph of a polynomial function that s...
 2.2.2.2.67: In Exercises 6568, sketch the graph of a polynomial function that s...
 2.2.2.2.68: In Exercises 6568, sketch the graph of a polynomial function that s...
 2.2.2.2.69: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.70: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.71: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.72: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.73: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.74: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.75: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.76: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.77: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.78: In Exercises 6978, sketch the graph of the function by (a) applying...
 2.2.2.2.79: In Exercises 7982, (a) use the Intermediate Value Theorem and a gra...
 2.2.2.2.80: In Exercises 7982, (a) use the Intermediate Value Theorem and a gra...
 2.2.2.2.81: In Exercises 7982, (a) use the Intermediate Value Theorem and a gra...
 2.2.2.2.82: In Exercises 7982, (a) use the Intermediate Value Theorem and a gra...
 2.2.2.2.83: In Exercises 83 90, use a graphing utility to graph the function. I...
 2.2.2.2.84: In Exercises 83 90, use a graphing utility to graph the function. I...
 2.2.2.2.85: In Exercises 83 90, use a graphing utility to graph the function. I...
 2.2.2.2.86: In Exercises 83 90, use a graphing utility to graph the function. I...
 2.2.2.2.87: In Exercises 83 90, use a graphing utility to graph the function. I...
 2.2.2.2.88: In Exercises 83 90, use a graphing utility to graph the function. I...
 2.2.2.2.89: In Exercises 83 90, use a graphing utility to graph the function. I...
 2.2.2.2.90: In Exercises 83 90, use a graphing utility to graph the function. I...
 2.2.2.2.91: Numerical and Graphical Analysis An open box is to be made from a s...
 2.2.2.2.92: Geometry An open box with locking tabs is to be made from a square ...
 2.2.2.2.93: Revenue The total revenue (in millions of dollars) for a company is...
 2.2.2.2.94: Environment The growth of a red oak tree is approximated by the fun...
 2.2.2.2.95: Data Analysis In Exercises 9598, use the table, which shows the med...
 2.2.2.2.96: Data Analysis In Exercises 9598, use the table, which shows the med...
 2.2.2.2.97: Data Analysis In Exercises 9598, use the table, which shows the med...
 2.2.2.2.98: Data Analysis In Exercises 9598, use the table, which shows the med...
 2.2.2.2.99: True or False? In Exercises 99104, determine whether the statement ...
 2.2.2.2.100: True or False? In Exercises 99104, determine whether the statement ...
 2.2.2.2.101: True or False? In Exercises 99104, determine whether the statement ...
 2.2.2.2.102: True or False? In Exercises 99104, determine whether the statement ...
 2.2.2.2.103: True or False? In Exercises 99104, determine whether the statement ...
 2.2.2.2.104: True or False? In Exercises 99104, determine whether the statement ...
 2.2.2.2.105: Library of Parent Functions In Exercises 105107, determine which po...
 2.2.2.2.106: Library of Parent Functions In Exercises 105107, determine which po...
 2.2.2.2.107: Library of Parent Functions In Exercises 105107, determine which po...
 2.2.2.2.108: In Exercises 108113, let and Find the indicated value.
 2.2.2.2.109: In Exercises 108113, let and Find the indicated value.
 2.2.2.2.110: In Exercises 108113, let and Find the indicated value.
 2.2.2.2.111: In Exercises 108113, let and Find the indicated value.
 2.2.2.2.112: In Exercises 108113, let and Find the indicated value.
 2.2.2.2.113: In Exercises 108113, let and Find the indicated value.
 2.2.2.2.114: In Exercises 114117, solve the inequality and sketch the solution o...
 2.2.2.2.115: In Exercises 114117, solve the inequality and sketch the solution o...
 2.2.2.2.116: In Exercises 114117, solve the inequality and sketch the solution o...
 2.2.2.2.117: In Exercises 114117, solve the inequality and sketch the solution o...
Solutions for Chapter 2.2: Polynomial Functions of Higher Degree
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 2.2: Polynomial Functions of Higher Degree
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 117 problems in chapter 2.2: Polynomial Functions of Higher Degree have been answered, more than 36196 students have viewed full stepbystep solutions from this chapter. Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. This textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5. Chapter 2.2: Polynomial Functions of Higher Degree includes 117 full stepbystep solutions.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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

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!

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

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).

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].

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.

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.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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

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

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

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

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.