 2.2.1: The graph of a function is the graph of its ______________.
 2.2.2: If any vertical line intersects a graph ______________, the graph d...
 2.2.3: The shaded set of numbers shown on the xaxis can be expressed in i...
 2.2.4: The shaded set of numbers shown on the yaxis can be expressed in i...
 2.2.5: f(x) = x2 , g(x) = x2 + 1
 2.2.6: f(x) = x2 , g(x) = x2  2
 2.2.7: f(x) = x , g(x) = x  2
 2.2.8: f(x) = x , g(x) = x + 1
 2.2.9: f(x) = x3 , g(x) = x3 + 2
 2.2.10: f(x) = x3 , g(x) = x3  1
 2.2.11: In Exercises 1118, use the vertical line test to identify graphs in...
 2.2.12: In Exercises 1118, use the vertical line test to identify graphs in...
 2.2.13: In Exercises 1118, use the vertical line test to identify graphs in...
 2.2.14: In Exercises 1118, use the vertical line test to identify graphs in...
 2.2.15: In Exercises 1118, use the vertical line test to identify graphs in...
 2.2.16: In Exercises 1118, use the vertical line test to identify graphs in...
 2.2.17: In Exercises 1118, use the vertical line test to identify graphs in...
 2.2.18: In Exercises 1118, use the vertical line test to identify graphs in...
 2.2.19: f(2)
 2.2.20: f(2)
 2.2.21: f(4)
 2.2.22: f(4)
 2.2.23: f(3)
 2.2.24: f(1)
 2.2.25: Find g(4).
 2.2.26: Find g(2).
 2.2.27: Find g(10).
 2.2.28: Find g(10).
 2.2.29: For what value of x is g(x) = 1?
 2.2.30: For what value of x is g(x) = 1?
 2.2.31: In Exercises 3140, use the graph of each function to identify its d...
 2.2.32: In Exercises 3140, use the graph of each function to identify its d...
 2.2.33: In Exercises 3140, use the graph of each function to identify its d...
 2.2.34: In Exercises 3140, use the graph of each function to identify its d...
 2.2.35: In Exercises 3140, use the graph of each function to identify its d...
 2.2.36: In Exercises 3140, use the graph of each function to identify its d...
 2.2.37: In Exercises 3140, use the graph of each function to identify its d...
 2.2.38: In Exercises 3140, use the graph of each function to identify its d...
 2.2.39: In Exercises 3140, use the graph of each function to identify its d...
 2.2.40: In Exercises 3140, use the graph of each function to identify its d...
 2.2.41: Use the graph of f to determine each of the following. Where applic...
 2.2.42: Use the graph of f to determine each of the following. Where applic...
 2.2.43: a. Find and interpret G(30). Identify this information as a point o...
 2.2.44: a. Find and interpret G(10). Identify this information as a point o...
 2.2.45: Find and interpret f(20). Identify this information as a point on t...
 2.2.46: Find and interpret f(50). Identify this information as a point on t...
 2.2.47: For what value of x does the graph reach its lowest point? Use the ...
 2.2.48: Use the graph to identify two different ages for which drivers have...
 2.2.49: Find f(3). What does this mean in terms of the variables in this si...
 2.2.50: Find f(3.5). What does this mean in terms of the variables in this ...
 2.2.51: What is the cost of mailing a letter that weighs 1.5 ounces?
 2.2.52: What is the cost of mailing a letter that weighs 1.8 ounces?
 2.2.53: What is the graph of a function?
 2.2.54: Explain how the vertical line test is used to determine whether a g...
 2.2.55: Explain how to identify the domain and range of a function from its...
 2.2.56: Use a graphing utility to verify the pairs of graphs that you drew ...
 2.2.57: The function f(x) = 0.00002x3 + 0.008x2  0.3x + 6.95 models the n...
 2.2.58: I knew how to use point plotting to graph the equation y = x2  1, ...
 2.2.59: The graph of my function revealed aspects of its behavior that were...
 2.2.60: I graphed a function showing how paid vacation days depend on the n...
 2.2.61: I graphed a function showing how the number of annual physician vis...
 2.2.62: The graph of every line is a function.
 2.2.63: A horizontal line can intersect the graph of a function in more tha...
 2.2.64: The domain of f is [4, 4].
 2.2.65: The range of f is [2, 2].
 2.2.66: f(1)  f(4) = 2
 2.2.67: f(0) = 2.1
 2.2.68: Find 2f(1.5) + f(0.9)  [f(p)] 2 + f(3) , f(1) # f(p).
 2.2.69: Find 2f(2.5)  f(1.9)  [f(p)] 2 + f(3) , f(1) # f(p).
 2.2.70: Is {(1, 1), (2, 2), (3, 3), (4, 4)} a function? (Section 2.1, Examp...
 2.2.71: Solve: 12  2(3x + 1) = 4x  5. (Section 1.4, Example 3)
 2.2.72: The length of a rectangle exceeds 3 times the width by 8 yards. If ...
 2.2.73: If f(x) = 4 x  3 , why must 3 be excluded from the domain of f ?
 2.2.74: If f(x) = x2 + x and g(x) = x  5, find f(4) + g(4).
 2.2.75: Simplify: 2.6x2 + 49x + 3994  (0.6x2 + 7x + 2412).
Solutions for Chapter 2.2: Graphs of Functions
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 2.2: Graphs of Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.2: Graphs of Functions includes 75 full stepbystep solutions. Since 75 problems in chapter 2.2: Graphs of Functions have been answered, more than 49510 students have viewed full stepbystep solutions from this chapter. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6.

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!

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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

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.

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.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

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

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

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.

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

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

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

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.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.