 2.1.1: State the domain and range of each relation. Then determine whether...
 2.1.2: State the domain and range of each relation. Then determine whether...
 2.1.3: State the domain and range of each relation. Then determine whether...
 2.1.4: Identify the domain and range. Assume that the January temperatures...
 2.1.5: Write a relation of ordered pairs for the data
 2.1.6: Graph the relation. Is this relation a function?
 2.1.7: Graph each relation or equation and find the domain and range. Then...
 2.1.8: Graph each relation or equation and find the domain and range. Then...
 2.1.9: Graph each relation or equation and find the domain and range. Then...
 2.1.10: Graph each relation or equation and find the domain and range. Then...
 2.1.11: Graph each relation or equation and find the domain and range. Then...
 2.1.12: Graph each relation or equation and find the domain and range. Then...
 2.1.13: State the domain and range of each relation. Then determine whether...
 2.1.14: State the domain and range of each relation. Then determine whether...
 2.1.15: State the domain and range of each relation. Then determine whether...
 2.1.16: State the domain and range of each relation. Then determine whether...
 2.1.17: State the domain and range of each relation. Then determine whether...
 2.1.18: State the domain and range of each relation. Then determine whether...
 2.1.19: State the domain and range of each relation. Then determine whether...
 2.1.20: State the domain and range of each relation. Then determine whether...
 2.1.21: State the domain and range of each relation. Then determine whether...
 2.1.22: State the domain and range of each relation. Then determine whether...
 2.1.23: Graph each relation or equation and find the domain and range. Then...
 2.1.24: Graph each relation or equation and find the domain and range. Then...
 2.1.25: Graph each relation or equation and find the domain and range. Then...
 2.1.26: Graph each relation or equation and find the domain and range. Then...
 2.1.27: Graph each relation or equation and find the domain and range. Then...
 2.1.28: Graph each relation or equation and find the domain and range. Then...
 2.1.29: Graph each relation or equation and find the domain and range. Then...
 2.1.30: Graph each relation or equation and find the domain and range. Then...
 2.1.31: Graph each relation or equation and find the domain and range. Then...
 2.1.32: Graph each relation or equation and find the domain and range. Then...
 2.1.33: Graph each relation or equation and find the domain and range. Then...
 2.1.34: Graph each relation or equation and find the domain and range. Then...
 2.1.35: Find each value if f(x) = 3x  5 and g(x) = x2  x
 2.1.36: Find each value if f(x) = 3x  5 and g(x) = x2  x
 2.1.37: Find each value if f(x) = 3x  5 and g(x) = x2  x
 2.1.38: Find each value if f(x) = 3x  5 and g(x) = x2  x
 2.1.39: Find each value if f(x) = 3x  5 and g(x) = x2  x
 2.1.40: Find each value if f(x) = 3x  5 and g(x) = x2  x
 2.1.41: Find the value of f(x) = 3x + 2 when x = 2.
 2.1.42: What is g(4) if g(x) = x2  5?
 2.1.43: Make a graph of the data with home runs on the horizontal axis and ...
 2.1.44: Identify the domain and range
 2.1.45: Does the graph represent a function? Explain your reasoning.
 2.1.46: Write a relation to represent the data
 2.1.47: Graph the relation
 2.1.48: Identify the domain and range
 2.1.49: Is the relation a function? Explain your reasoning.
 2.1.50: Write a relation to represent the data.
 2.1.51: Graph the relation
 2.1.52: Identify the domain and range. Determine whether the relation is di...
 2.1.53: Is the relation a function? Explain your reasoning
 2.1.54: Chaz has a collection of 15 audio books. After he gets a parttime ...
 2.1.55: Write a relation of four ordered pairs that is not a function. Expl...
 2.1.56: Teisha and Molly are finding g(2a) for the function g(x) = x2 + x ...
 2.1.57: If f(3a  1) = 12a  7, find one possible expression for f(x).
 2.1.58: Use the information about animal lifetimes on page 58 to explain ho...
 2.1.59: If g(x) = x2, which expression is equal to g(x + 1)? A 1 B x2 + 1 C...
 2.1.60: Which set of dimensions represent a triangle similar to the triangl...
 2.1.61: Solve each inequality
 2.1.62: Solve each inequality
 2.1.63: Solve each inequality
 2.1.64: Javier had $25.04 when he went to the mall. His friend Sally had $3...
 2.1.65: Simplify each expression
 2.1.66: Simplify each expression
 2.1.67: Solve each equation. Check your solution.
 2.1.68: Solve each equation. Check your solution.
 2.1.69: Solve each equation. Check your solution.
 2.1.70: Solve each equation. Check your solution.
Solutions for Chapter 2.1: Relations and Functions
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 2.1: Relations and Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. This expansive textbook survival guide covers the following chapters and their solutions. Since 70 problems in chapter 2.1: Relations and Functions have been answered, more than 44295 students have viewed full stepbystep solutions from this chapter. Chapter 2.1: Relations and Functions includes 70 full stepbystep solutions.

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

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.)

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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.

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.

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

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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

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).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!