 1.3.1: In the rectangular coordinate system, the horizontal number line is...
 1.3.2: In the rectangular coordinate system, the vertical number line is c...
 1.3.3: In the rectangular coordinate system, the point of intersection of ...
 1.3.4: The axes of the rectangular coordinate system divide the plane into...
 1.3.5: The first number in an ordered pair such as (8, 3) is called the __...
 1.3.6: The ordered pair (4, 19) is a/an ______________ of the equation y =...
 1.3.7: (4, 1)
 1.3.8: (3, 2)
 1.3.9: (4, 0)
 1.3.10: (0, 3)
 1.3.11: y = x2  4
 1.3.12: y = x2  9
 1.3.13: y = x  2
 1.3.14: y = x + 2
 1.3.15: y = 2x + 1
 1.3.16: y = 2x  4
 1.3.17: y =  1 2 x
 1.3.18: y =  1 2 x + 2
 1.3.19: y = x + 1
 1.3.20: y = x  1
 1.3.21: y = 2 x
 1.3.22: y = 2 x
 1.3.23: y = x2
 1.3.24: y =  1 2 x2
 1.3.25: y = x3
 1.3.26: y = x3  1
 1.3.27: [5, 5, 1] by [5, 5, 1]
 1.3.28: [10, 10, 2] by [4, 4, 2]
 1.3.29: [20, 80, 10] by [30, 70, 10]
 1.3.30: [40, 40, 20] by [1000, 1000, 100]
 1.3.31: Which equation corresponds to Y2 in the table? a. y2 = x + 8 b. y2 ...
 1.3.32: Which equation corresponds to Y1 in the table? a. y1 = 3x b. y1 = ...
 1.3.33: Does the graph of Y2 pass through the origin?
 1.3.34: Does the graph of Y1 pass through the origin?
 1.3.35: At which point does the graph of Y2 cross the xaxis?
 1.3.36: At which point does the graph of Y2 cross the yaxis?
 1.3.37: At which points do the graphs of Y1 and Y2 intersect?
 1.3.38: For which values of x is Y1 = Y2?
 1.3.39: The yvalue is four more than twice the xvalue.
 1.3.40: The yvalue is the difference between four and twice the xvalue.
 1.3.41: The yvalue is three decreased by the square of the xvalue.
 1.3.42: The yvalue is two more than the square of the xvalue.
 1.3.43: y = 5 (Let x = 3, 2, 1, 0, 1, 2, and 3.)
 1.3.44: y = 1 (Let x = 3, 2, 1, 0, 1, 2, and 3.)
 1.3.45: y = 1 x (Let x = 2, 1,  1 2 ,  1 3 , 1 3 , 1 2 , 1, and 2.)
 1.3.46: y =  1 x (Let x = 2, 1,  1 2 ,  1 3 , 1 3 , 1 2 , 1, and 2.)
 1.3.47: Estimate the top marginal tax rate in 2010.
 1.3.48: Estimate the top marginal tax rate in 1925.
 1.3.49: For the period shown, during which year did the United States have ...
 1.3.50: For the period from 1950 through 2010, during which year did the Un...
 1.3.51: For the period shown, during which tenyear period did the top marg...
 1.3.52: For the period shown, during which fiveyear period did the top mar...
 1.3.53: At which age, estimated to the nearest year, do women have the leas...
 1.3.54: At which age do men have the greatest number of awakenings during t...
 1.3.55: Estimate, to the nearest tenth, the difference between the average ...
 1.3.56: Estimate, to the nearest tenth, the difference between the average ...
 1.3.57: As the blizzard got worse, the snow fell harder and harder.
 1.3.58: The snow fell more and more softly.
 1.3.59: It snowed hard, but then it stopped. After a short time, the snow s...
 1.3.60: It snowed softly, and then it stopped. After a short time, the snow...
 1.3.61: An airplane flew from Miami to San Francisco. a. Planes Height Seco...
 1.3.62: At noon, you begin to breathe in. a. Volume of Air in Lungs Time af...
 1.3.63: Measurements are taken of a persons height from birth to age 100. a...
 1.3.64: You begin your bike ride by riding down a hill. Then you ride up an...
 1.3.65: What is the rectangular coordinate system?
 1.3.66: Explain how to plot a point in the rectangular coordinate system. G...
 1.3.67: Explain why (5, 2) and (2, 5) do not represent the same point.
 1.3.68: Explain how to graph an equation in the rectangular coordinate system.
 1.3.69: What does a [20, 2, 1] by [4, 5, 0.5] viewing rectangle mean?
 1.3.70: Checking Account Balance
 1.3.71: Hair Length
 1.3.72: Use a graphing utility to verify each of your handdrawn graphs in ...
 1.3.73: The rectangular coordinate system provides a geometric picture of w...
 1.3.74: There is something wrong with my graphing utility because it is not...
 1.3.75: A horizontal line is not a graph that tells the story of the number...
 1.3.76: I told my story with a graph, so I can be confident that there is a...
 1.3.77: If the product of a points coordinates is positive, the point must ...
 1.3.78: If a point is on the xaxis, it is neither up nor down, so x = 0.
 1.3.79: If a point is on the yaxis, its xcoordinate must be 0.
 1.3.80: The ordered pair (2, 5) satisfies 3y  2x = 4.
 1.3.81: You park your car at the garage for four hours on Tuesday and five ...
 1.3.82: On Thursday, you paid $12 for parking at the garage. Describe how l...
 1.3.83: Find the absolute value: 14.3. (Section 1.2, Example 1)
 1.3.84: Simplify: [12  (13  17)]  [9  (6  10)] (Section 1.2, Examples ...
 1.3.85: Simplify: 6x  5(4x + 3)  10. (Section 1.2, Example 13)
 1.3.86: If 9 is substituted for x in the equation 4x  3 = 5x + 6, is the ...
 1.3.87: Simplify: 13  3(x + 2).
 1.3.88: Simplify: 10a 3x + 1 2 b.
Solutions for Chapter 1.3: Graphing Equations
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 1.3: Graphing Equations
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Since 88 problems in chapter 1.3: Graphing Equations have been answered, more than 29683 students have viewed full stepbystep solutions from this chapter. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. Chapter 1.3: Graphing Equations includes 88 full stepbystep solutions.

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

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.)

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

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

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

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

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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

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

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

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

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).