 2.1: Determine whether the statement is true or false.The greatest integ...
 2.2: Determine whether the statement is true or false.In general, for fu...
 2.3: Determine whether the statement is true or false.The graph of y = 1...
 2.4: Determine whether the statement is true or false.The graph of y = ...
 2.5: Determine the intervals on which the function is (a) increasing, (b...
 2.6: Determine the intervals on which the function is (a) increasing, (b...
 2.7: Graph the function. Estimate the intervals on which the function is...
 2.8: Graph the function. Estimate the intervals on which the function is...
 2.9: Use a graphing calculator to find the intervals on which the functi...
 2.10: Use a graphing calculator to find the intervals on which the functi...
 2.11: Use a graphing calculator to find the intervals on which the functi...
 2.12: Use a graphing calculator to find the intervals on which the functi...
 2.13: Tablecloth Area. A seamstress uses 20 ft of lace to trim the edges ...
 2.14: nscribed Rectangle. A rectangle is inscribed in a semicircle of rad...
 2.15: Dog Pen. Mamie has 66 ft of fencing with which to enclose a rectang...
 2.16: Minimizing Surface Area. A container firm is designing an opentop ...
 2.17: Graph each of the following. [2.1]f 1x2 = ex, 12 x + 1,for x 4,fo...
 2.18: Graph each of the following. [2.1]f 1x2 = x3, x ,2x  1,for x 6 2,...
 2.19: Graph each of the following. [2.1]f 1x2 = x2  1x + 1 ,3,for x 1,f...
 2.20: Graph each of the following. [2.1]f 1x2 = x
 2.21: Graph each of the following. [2.1]f 1x2 = x  3
 2.22: Graph each of the following. [2.1]For the function in Exercise 18, ...
 2.23: Graph each of the following. [2.1]For the function in Exercise 19, ...
 2.24: Given that f 1x2 = 2x  2 and g1x2 = x2  1, find each of the follo...
 2.25: Given that f 1x2 = 2x  2 and g1x2 = x2  1, find each of the follo...
 2.26: Given that f 1x2 = 2x  2 and g1x2 = x2  1, find each of the follo...
 2.27: For each pair of functions in Exercises 27 and 28: a) Find the doma...
 2.28: For each pair of functions in Exercises 27 and 28: a) Find the doma...
 2.29: For each pair of functions in Exercises 27 and 28: a) Find the doma...
 2.30: For each function f, construct and simplify the difference quotient...
 2.31: For each function f, construct and simplify the difference quotient...
 2.32: For each function f, construct and simplify the difference quotient...
 2.33: Given that f 1x2 = 2x  1, g1x2 = x2 + 4, and h1x2 = 3  x3 , find ...
 2.34: Given that f 1x2 = 2x  1, g1x2 = x2 + 4, and h1x2 = 3  x3 , find ...
 2.35: Given that f 1x2 = 2x  1, g1x2 = x2 + 4, and h1x2 = 3  x3 , find ...
 2.36: Given that f 1x2 = 2x  1, g1x2 = x2 + 4, and h1x2 = 3  x3 , find ...
 2.37: Given that f 1x2 = 2x  1, g1x2 = x2 + 4, and h1x2 = 3  x3 , find ...
 2.38: Given that f 1x2 = 2x  1, g1x2 = x2 + 4, and h1x2 = 3  x3 , find ...
 2.39: Given that f 1x2 = 2x  1, g1x2 = x2 + 4, and h1x2 = 3  x3 , find ...
 2.40: Given that f 1x2 = 2x  1, g1x2 = x2 + 4, and h1x2 = 3  x3 , find ...
 2.41: n Exercises 41 and 42, for the pair of functions: a) Find 1f g21x2 ...
 2.42: n Exercises 41 and 42, for the pair of functions: a) Find 1f g21x2 ...
 2.43: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. [2.3]h1x2 = 25x + 2
 2.44: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. [2.3]h1x2 = 415x  1...
 2.45: Graph the given equation and determine visually whether it is symme...
 2.46: Graph the given equation and determine visually whether it is symme...
 2.47: Graph the given equation and determine visually whether it is symme...
 2.48: Graph the given equation and determine visually whether it is symme...
 2.49: Graph the given equation and determine visually whether it is symme...
 2.50: Graph the given equation and determine visually whether it is symme...
 2.51: Determine visually whether the function is even, odd, or neither ev...
 2.52: Determine visually whether the function is even, odd, or neither ev...
 2.53: Determine visually whether the function is even, odd, or neither ev...
 2.54: Determine visually whether the function is even, odd, or neither ev...
 2.55: Determine whether the function is even, odd, or neither even nor od...
 2.56: Determine whether the function is even, odd, or neither even nor od...
 2.57: Determine whether the function is even, odd, or neither even nor od...
 2.58: Determine whether the function is even, odd, or neither even nor od...
 2.59: Determine whether the function is even, odd, or neither even nor od...
 2.60: Determine whether the function is even, odd, or neither even nor od...
 2.61: Write an equation for a function that has a graph with the given ch...
 2.62: Write an equation for a function that has a graph with the given ch...
 2.63: Write an equation for a function that has a graph with the given ch...
 2.64: A graph of y = f 1x2 is shown below. No formula for f is given. Gra...
 2.65: A graph of y = f 1x2 is shown below. No formula for f is given. Gra...
 2.66: A graph of y = f 1x2 is shown below. No formula for f is given. Gra...
 2.67: A graph of y = f 1x2 is shown below. No formula for f is given. Gra...
 2.68: Find an equation of variation for the given situation. [2.6]y varie...
 2.69: Find an equation of variation for the given situation. [2.6]y varie...
 2.70: Find an equation of variation for the given situation. [2.6]y varie...
 2.71: Find an equation of variation for the given situation. [2.6]y varie...
 2.72: Find an equation of variation for the given situation. [2.6]y varie...
 2.73: Find an equation of variation for the given situation. [2.6]y varie...
 2.74: Pumping Time. The time t required to empty a tank varies inversely ...
 2.75: Test Score. The score N on a test varies directly as the number of ...
 2.76: Power of Electric Current. The power P expended by heat in an elect...
 2.77: For f 1x2 = x + 1 and g1x2 = 2x, the domain of 1g f 21x2 is which o...
 2.78: For b 7 0, the graph of y = f 1x2 + b is the graph of y = f 1x2 shi...
 2.79: The graph of the function f is shown below. 2 2 1 4 2 2 4 543 1 1 3...
 2.80: Prove that the sum of two odd functions is odd. [2.2], [2.4]
 2.81: Describe how the graph of y = f 1x2 is obtained from the graph of...
 2.82: Given that f 1x2 = 4x3  2x + 7, find each of the following. Then d...
 2.83: Given the graph of y = f 1x2, explain and contrast the effect of th...
 2.84: Consider the constant function f 1x2 = 0. Determine whether the gra...
 2.85: Describe conditions under which you would know whether a polynomial...
 2.86: If y varies directly as x2 , explain why doubling x would not cause...
 2.87: If y varies directly as x and x varies inversely as z, how does y v...
Solutions for Chapter 2: More on Functions
Full solutions for College Algebra: Graphs and Models  5th Edition
ISBN: 9780321783950
Solutions for Chapter 2: More on Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra: Graphs and Models, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2: More on Functions includes 87 full stepbystep solutions. Since 87 problems in chapter 2: More on Functions have been answered, more than 27095 students have viewed full stepbystep solutions from this chapter. College Algebra: Graphs and Models was written by and is associated to the ISBN: 9780321783950.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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

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].

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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

Outer product uv T
= column times row = rank one matrix.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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