 2.6.1: Graph each function. Identify the domain and range.
 2.6.2: Graph each function. Identify the domain and range.
 2.6.3: Graph each function. Identify the domain and range.
 2.6.4: Graph each function. Identify the domain and range.
 2.6.5: Graph each function. Identify the domain and range.
 2.6.6: Graph each function. Identify the domain and range.
 2.6.7: Graph each function. Identify the domain and range.
 2.6.8: Graph each function. Identify the domain and range.
 2.6.9: Identify each function as S for step, C for constant, A for absolut...
 2.6.10: Identify each function as S for step, C for constant, A for absolut...
 2.6.11: What type of special function models this situation?
 2.6.12: Draw a graph of a function that represents this situation.
 2.6.13: Use the graph to find the cost of parking there for 4 _1 2 hours.
 2.6.14: Graph each function. Identify the domain and range.
 2.6.15: Graph each function. Identify the domain and range.
 2.6.16: Graph each function. Identify the domain and range.
 2.6.17: Graph each function. Identify the domain and range.
 2.6.18: Graph each function. Identify the domain and range.
 2.6.19: Graph each function. Identify the domain and range.
 2.6.20: Graph each function. Identify the domain and range.
 2.6.21: Graph each function. Identify the domain and range.
 2.6.22: Graph each function. Identify the domain and range.
 2.6.23: Graph each function. Identify the domain and range.
 2.6.24: Graph each function. Identify the domain and range.
 2.6.25: Graph each function. Identify the domain and range.
 2.6.26: Graph each function. Identify the domain and range.
 2.6.27: Graph each function. Identify the domain and range.
 2.6.28: Identify each function as S for step, C for constant, A for absolut...
 2.6.29: Identify each function as S for step, C for constant, A for absolut...
 2.6.30: Identify each function as S for step, C for constant, A for absolut...
 2.6.31: Identify each function as S for step, C for constant, A for absolut...
 2.6.32: Identify each function as S for step, C for constant, A for absolut...
 2.6.33: Identify each function as S for step, C for constant, A for absolut...
 2.6.34: Springfield High Schools theater can hold 250 students. The drama c...
 2.6.35: Graph each function. Identify the domain and range.
 2.6.36: Graph each function. Identify the domain and range.
 2.6.37: Graph each function. Identify the domain and range.
 2.6.38: Graph each function. Identify the domain and range.
 2.6.39: Graph each function. Identify the domain and range.
 2.6.40: Graph each function. Identify the domain and range.
 2.6.41: Graph a step function that represents this situation.
 2.6.42: How much would a call that lasts 9 minutes and 40 seconds cost?
 2.6.43: Write an absolute value function for the difference between the num...
 2.6.44: What is an appropriate domain for the function?
 2.6.45: Use the domain to graph the function.
 2.6.46: According to the terms of Lavons insurance plan, he must pay the fi...
 2.6.47: Write a function involving absolute value for which f(2) = 3.
 2.6.48: Find a counterexample to the statement To find the greatest integer...
 2.6.49: Graph x + y = 3.
 2.6.50: Use the information on page 95 to explain how step functions apply ...
 2.6.51: For which function does f(_1 2 ) 1? A f(x) = 2x C f(x) = x B f(x)...
 2.6.52: For which function is the range {y y 0}? F f(x) = x G f(x) = x H f...
 2.6.53: For which function is the range {y y 0}? F f(x) = x G f(x) = x H f...
 2.6.54: For Exercises 5456, use the table that shows the life expectancy fo...
 2.6.55: For Exercises 5456, use the table that shows the life expectancy fo...
 2.6.56: For Exercises 5456, use the table that shows the life expectancy fo...
 2.6.57: Write an equation in slopeintercept form that satisfies each set o...
 2.6.58: Write an equation in slopeintercept form that satisfies each set o...
 2.6.59: Solve each inequality. Graph the solution set
 2.6.60: Solve each inequality. Graph the solution set
 2.6.61: Determine whether (0, 0) satisfies each inequality. Write yes or no
 2.6.62: Determine whether (0, 0) satisfies each inequality. Write yes or no
 2.6.63: Determine whether (0, 0) satisfies each inequality. Write yes or no
 2.6.64: Determine whether (0, 0) satisfies each inequality. Write yes or no
 2.6.65: Determine whether (0, 0) satisfies each inequality. Write yes or no
 2.6.66: Determine whether (0, 0) satisfies each inequality. Write yes or no
Solutions for Chapter 2.6: Special Functions
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 2.6: Special Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. Chapter 2.6: Special Functions includes 66 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. Since 66 problems in chapter 2.6: Special Functions have been answered, more than 46769 students have viewed full stepbystep solutions from this chapter.

Column space C (A) =
space of all combinations of the columns of A.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex 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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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

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.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

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

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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

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 •

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

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.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.