Calculators. See Graphing calculators

Calories, minimizing, 574–575

Candy consumption, 20, 27

Car(s), counting possible selections of, 767–768

Carbon dating, 470–471

Carcharodon megalodon, 249, 250–251

Card(s), drawing from a deck, 782–783

Cardano, Gerolamo, 376

Carnarvon, Lord, 462

Carrying capacity (M), 475, 482

Carter, Howard, 462

Cartesian plane. See Coordinate plane

CAT scans, 527, 534–535

Cayley, Arthur, 622

Center

• of an ellipse, 676

• of a circle, 191

• of a hyperbola, 691

Change-of-base formula, 467–468

Chapman, Helen, 198

Chessboard, grains of wheat on, 423

Chia Hsien, 760

Cholesterol-reducing drugs, 225–226

Circles, 191–192, 659

• general form for equation of, 193–194

• graphing, 192

• standard form for equation of, 191–192

• unit, 192

Closed interval, 8

Closure property of real numbers, 12

Coding messages, 621, 630–631

Coefficients

• binomial, 763–764

• leading, 31

• of a monomial, 30, 37

• of a polynomial, 31

Cofactors

• expanding by, 639

• in a matrix, 637–638

Coffee

• consumption of, 20, 27

• hot, cooling of, 456

Coin toss, 780

Column matrices, 590

Combinations, 771–773

Combined variation, 407–409

Combining functions, 281–284

Comentarii Academia Petropolitanae (Euler), 33

Common difference, of an arithmetic sequence, 729–730, 732

Common logarithms, 452–453

• digits and, 466–467

Common ratio, of a geometric sequence, 738–739

Commutative property of real numbers, 12

Complements of an event, probability of, 783–784

Completing the square, solving quadratic equations by, 109–111

Complex conjugate product theorem, 124

Complex fractions, 56–57

Complex numbers, 119–129

• adding and subtracting, 121

• conjugates of, 123–125

• defined, 120

• dividing, 123–125

• equality of, 121

• multiplying, 122–123

• real and imaginary parts of, 120–121

• standard form of, 120

Complex polynomials, 377

Complex zeros of a polynomial function, 376–383

• Conjugate Pairs Theorem and, 378–381

• finding, 380–381

Composite functions, 284–290

• applications of, 288–290

• decomposition of, 288

• domain of, 286–288

• evaluating, 285

Compound inequalities, 148–151

Compounding annually, 432

Compound interest, 431–434

Compound interest formula, 432

Compressing graphs of functions, 269–272

Computer graphics, 606, 614–616

Conditional equations, 82, 86

Conditional inequalities, 145

Conic sections, 658–714. See also Circles; Ellipses; Hyperbolas; Parabolas

• degenerate, 660

Conjugate(s), 67–68

• of complex numbers, 123–125

Conjugate axis, of a hyperbola, 691

Conjugate Pairs Theorem, 378–381

Consistent systems of linear equations in three variables, 530

Constant(s), 2

• gravitational, universal, 408

Constant functions, 235–237, 249, 257

Constant of variation (proportionality), 404

Constant term, 31

• of a polynomial function, 332

Constraints, 571

Continuous compound interest formula, 434–436

• exponential and logarithmic forms of, 454–455

Conway, John, 202

Coordinate(s), 6

Coordinate axes, 175

Coordinate line, 175. See also Number line

Coordinate plane, 175–184. See also Graphs and graphing

• Descartes’s discovery of, 175

• distance between two points in, 178–180

• midpoint of a line segment and, 180–181

Cormack, Allan, 527

Corner point, of the solution set of a system of inequalities, 563

Correspondence diagrams, 216

Costs, fixed, marginal, and variable, 227

Coughing, 235, 239

Counting principles, 767–777

• choosing method to use, 774–775

• combinations and, 771–773

• distinguishable permutations and, 773–774

• fundamental, 767–769

• permutations and, 769–771

Cramer, Gabriel, 640

Cramer’s Rule, 640–644

Cricket chirps, temperature and, 2, 15–16

Crude oil consumption, 359–360

Cryptography, 621, 630–631

Cube(s), difference and sum of, factoring, 45–46

Cube root(s), 64

Cube root function, 251–252, 258

Cubic polynomials, 333

Cubing function, 257

• graphing, 240–241

Current (electric), alternating, 119, 125