 4.1.1: Terry is skiing down a steep hill. Terrys elevation, E(t), in feet ...
 4.1.2: Jessica is walking home from a friends house. After 2 minutes she i...
 4.1.3: A boat is 100 miles away from the marina, sailing directly toward i...
 4.1.4: If the graphs of two linear functions are perpendicular, describe t...
 4.1.5: If a horizontal line has the equation f(x) = a and a vertical line ...
 4.1.6: For the following exercises, determine whether the equation of the ...
 4.1.7: For the following exercises, determine whether the equation of the ...
 4.1.8: For the following exercises, determine whether the equation of the ...
 4.1.9: For the following exercises, determine whether the equation of the ...
 4.1.10: For the following exercises, determine whether the equation of the ...
 4.1.11: For the following exercises, determine whether the equation of the ...
 4.1.12: For the following exercises, determine whether the equation of the ...
 4.1.13: For the following exercises, determine whether the equation of the ...
 4.1.14: For the following exercises, determine whether each function is inc...
 4.1.15: For the following exercises, determine whether each function is inc...
 4.1.16: For the following exercises, determine whether each function is inc...
 4.1.17: For the following exercises, determine whether each function is inc...
 4.1.18: For the following exercises, determine whether each function is inc...
 4.1.19: For the following exercises, determine whether each function is inc...
 4.1.20: For the following exercises, determine whether each function is inc...
 4.1.21: For the following exercises, determine whether each function is inc...
 4.1.22: For the following exercises, determine whether each function is inc...
 4.1.23: For the following exercises, determine whether each function is inc...
 4.1.24: For the following exercises, find the slope of the line that passes...
 4.1.25: For the following exercises, find the slope of the line that passes...
 4.1.26: For the following exercises, find the slope of the line that passes...
 4.1.27: For the following exercises, find the slope of the line that passes...
 4.1.28: For the following exercises, find the slope of the line that passes...
 4.1.29: For the following exercises, given each set of information, find a ...
 4.1.30: For the following exercises, given each set of information, find a ...
 4.1.31: For the following exercises, given each set of information, find a ...
 4.1.32: For the following exercises, given each set of information, find a ...
 4.1.33: For the following exercises, given each set of information, find a ...
 4.1.34: For the following exercises, given each set of information, find a ...
 4.1.35: For the following exercises, given each set of information, find a ...
 4.1.36: For the following exercises, given each set of information, find a ...
 4.1.37: For the following exercises, determine whether the lines given by t...
 4.1.38: For the following exercises, determine whether the lines given by t...
 4.1.39: For the following exercises, determine whether the lines given by t...
 4.1.40: For the following exercises, determine whether the lines given by t...
 4.1.41: For the following exercises, find the x and yintercepts of each e...
 4.1.42: For the following exercises, find the x and yintercepts of each e...
 4.1.43: For the following exercises, find the x and yintercepts of each e...
 4.1.44: For the following exercises, find the x and yintercepts of each e...
 4.1.45: For the following exercises, find the x and yintercepts of each e...
 4.1.46: For the following exercises, find the x and yintercepts of each e...
 4.1.47: For the following exercises, use the descriptions of each pair of l...
 4.1.48: For the following exercises, use the descriptions of each pair of l...
 4.1.49: For the following exercises, use the descriptions of each pair of l...
 4.1.50: For the following exercises, use the descriptions of each pair of l...
 4.1.51: For the following exercises, use the descriptions of each pair of l...
 4.1.52: For the following exercises, write an equation for the line describ...
 4.1.53: For the following exercises, write an equation for the line describ...
 4.1.54: For the following exercises, write an equation for the line describ...
 4.1.55: For the following exercises, write an equation for the line describ...
 4.1.56: For the following exercises, find the slope of the lines graphed.
 4.1.57: For the following exercises, find the slope of the lines graphed.
 4.1.58: For the following exercises, write an equation for the lines graphed.
 4.1.59: For the following exercises, write an equation for the lines graphed.
 4.1.60: For the following exercises, write an equation for the lines graphed.
 4.1.61: For the following exercises, write an equation for the lines graphed.
 4.1.62: For the following exercises, write an equation for the lines graphed.
 4.1.63: For the following exercises, write an equation for the lines graphed.
 4.1.64: For the following exercises, match the given linear equation with i...
 4.1.65: For the following exercises, match the given linear equation with i...
 4.1.66: For the following exercises, match the given linear equation with i...
 4.1.67: For the following exercises, match the given linear equation with i...
 4.1.68: For the following exercises, match the given linear equation with i...
 4.1.69: For the following exercises, match the given linear equation with i...
 4.1.70: For the following exercises, sketch a line with the given features....
 4.1.71: For the following exercises, sketch a line with the given features....
 4.1.72: For the following exercises, sketch a line with the given features....
 4.1.73: For the following exercises, sketch a line with the given features....
 4.1.74: For the following exercises, sketch a line with the given features....
 4.1.75: For the following exercises, sketch a line with the given features....
 4.1.76: For the following exercises, sketch the graph of each equation. f(x...
 4.1.77: For the following exercises, sketch the graph of each equation. g(x...
 4.1.78: For the following exercises, sketch the graph of each equation.. h(...
 4.1.79: For the following exercises, sketch the graph of each equation.k(x)...
 4.1.80: For the following exercises, sketch the graph of each equation. f(t...
 4.1.81: For the following exercises, sketch the graph of each equation. . p...
 4.1.82: For the following exercises, sketch the graph of each equation. x = 3
 4.1.83: For the following exercises, sketch the graph of each equation.x = 2
 4.1.84: For the following exercises, sketch the graph of each equation.r(x)...
 4.1.85: For the following exercises, write the equation of the line shown i...
 4.1.86: For the following exercises, write the equation of the line shown i...
 4.1.87: For the following exercises, write the equation of the line shown i...
 4.1.88: For the following exercises, write the equation of the line shown i...
 4.1.89: For the following exercises, which of the tables could represent a ...
 4.1.90: For the following exercises, which of the tables could represent a ...
 4.1.91: For the following exercises, which of the tables could represent a ...
 4.1.92: For the following exercises, which of the tables could represent a ...
 4.1.93: For the following exercises, which of the tables could represent a ...
 4.1.94: For the following exercises, which of the tables could represent a ...
 4.1.95: For the following exercises, which of the tables could represent a ...
 4.1.96: For the following exercises, which of the tables could represent a ...
 4.1.97: For the following exercises, use a calculator or graphing technolog...
 4.1.98: For the following exercises, use a calculator or graphing technolog...
 4.1.99: For the following exercises, use a calculator or graphing technolog...
 4.1.100: For the following exercises, use a calculator or graphing technolog...
 4.1.101: For the following exercises, use a calculator or graphing technolog...
 4.1.102: Graph the linear function f on a domain of [10, 10] for the functio...
 4.1.103: Graph the linear function f on a domain of [0.1, 0.1] for the funct...
 4.1.104: Graph the linear function f where f(x) = ax + b on the same set of ...
 4.1.105: Find the value of x if a linear function goes through the following...
 4.1.106: Find the value of y if a linear function goes through the following...
 4.1.107: Find the equation of the line that passes through the following poi...
 4.1.108: Find the equation of the line that passes through the following poi...
 4.1.109: Find the equation of the line that passes through the following poi...
 4.1.110: Find the equation of the line parallel to the line g(x) = 0.01x + 2...
 4.1.111: Find the equation of the line perpendicular to the line g(x) = 0.01...
 4.1.112: For the following exercises, use the functions f(x) = 0.1x + 200 an...
 4.1.113: For the following exercises, use the functions f(x) = 0.1x + 200 an...
 4.1.114: At noon, a barista notices that she has $20 in her tip jar. If she ...
 4.1.115: A gym membership with two personal training sessions costs $125, wh...
 4.1.116: A clothing business finds there is a linear relationship between th...
 4.1.117: A phone company charges for service according to the formula: C(n) ...
 4.1.118: A farmer finds there is a linear relationship between the number of...
 4.1.119: A citys population in the year 1960 was 287,500. In 1989 the popula...
 4.1.120: A towns population has been growing linearly. In 2003, the populati...
 4.1.121: Suppose that average annual income (in dollars) for the years 1990 ...
 4.1.122: When temperature is 0 degrees Celsius, the Fahrenheit temperature i...
Solutions for Chapter 4.1: LINEAR FUNCTIONS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 4.1: LINEAR FUNCTIONS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781938168383. Since 122 problems in chapter 4.1: LINEAR FUNCTIONS have been answered, more than 30285 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra, edition: 1. Chapter 4.1: LINEAR FUNCTIONS includes 122 full stepbystep 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).

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.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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

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).

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

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.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.