Galilei, Galileo, 30

Die galvanische Kette mathematisch bearbeitet (Ohm), 539

Gateway Arch, 318

Gauss, Karl Friedrich, 377, 733

Gaussian elimination

• matrices and, 595–597

• systems of equations in three variables and, 528–529

Gauss-Jordan elimination, 597–600

GCF (greatest common monomial factor), 41, 42

General form

• of equation of a circle, 193–194

• of equation of a line, 203–205

• of equation of an ellipse, 682

• of equation of a parabola, 667–668

General term of a sequence, 716, 717–719

• of a geometric, 740

Geometric progressions. See Geometric sequences

Geometric sequences, 738–745

• applications involving, 744–745

• defined, 738

• finite, sum of, 743–744

• graphing, 741–742

• properties of, 741

• recursive definition of, 739

Geometric series, infinite, 746–747

Geometry formulas, 88

Geometry problems, modeling, 93–94

Gifts, distributing, 774

Global warming, 352

Golden ratio, 105, 114–115

Golden rectangle, 105, 114–115

GPS system, 690

Graphical method, for solving systems of linear equations, 515–516

Graphing calculators

• absolute value function on, 10

• binomial coefficients using, 761

• combinations using, 772

• complex conjugates on, 123

• complex numbers on, 121, 125

• determinants on, 639

• ellipses on, 679

• evaluating exponential functions using, 424

• exponential functions using, 435, 436

• exponents on, 6

• Factor Theorem and, 358–360

• fractions on, 62

• functions and, 264

• geometric sequences on, 744

• graphing using intercepts on, 204

• greatest integer function on, 256

• horizontal and vertical lines on, 203

• inequalities in two variables on, 561

• linear regression using, 208–209

• logarithmic functions and, 467

• matrices on, 591

• matrix addition on, 608

• matrix inverses on, 623

• matrix multiplication on, 612

• matrix subtraction on, 609

• one-to-one functions and, 301

• opposites on, 13

• order of operations and, 12

• parabolas on, 664, 665

• partial fractions on, 542

• permutations using, 771

• power functions on, 336

• rational functions and, 389, 391, 397

• rational numbers on, 62

• Remainder Theorem and, 357–358

• row-echelon form of a matrix on, 598

• row operations using, 593

• scales on, 178

• scientific notation on, 26

• semicircles on, 193

• sequences on, 717

• solution sets of a system of inequalities on, 562

• summation using, 723

• symmetry and, 189

• synthetic division using, 355

• systems of linear equations on, 516

• systems of nonlinear equations on, 553

• viewing rectangle of, 178

• zeros of a polynomial function on, 338, 366

Graphs and graphing, 185–197

• of an arithmetic sequence, 731–732

• of an ellipse, 679

• of circles, 191–192

• common logarithms and, 452

• defined, 6

• of exponential functions, 425–427

• of functions, 218, 222–225, 239–241. See also Transformations of functions; specific types of functions

• functions defined by, 218

• of geometric sequences, 741–742

• of a hyperbola, 697–698, 699

• intercepts of, 187

• of linear inequalities in two variables, 558–561

• of logarithmic functions, 448–452

• of ordered pairs, 176

• of a parabola, 663–665

• of piecewise functions, 255–256

• by plotting points, 186–187

• of polynomial functions, 342–345, 371–372

• of quadratic functions, 320–324

• of rational functions, 388–389, 392–398

• of semicircles, 193–194

• symmetry and, 188–191

• using translations, 388–389

Gravity, Newton’s Law of Universal Gravitation and, 403, 408–409

Greatest common monomial factor (GCF), 41, 42

Greatest integer function, 256, 258

Greenhouse effect, 352

Grid cells, 527, 534–535

Gross production matrix, 628

Grouping, factoring by, 46–47

Grouping symbols (()), 11

Growth

• exponential, 437–438, 469, 741

• linear, 431, 436–437

Growth models

• logarithmic, 499

• logistic, 475, 482

• power, 500