College Algebra, 2013a

More documents

Recommendations

Info

50 Relations and Functions 15. y 16. y 5 3 4 2 3 1 2 1 −3 −2 −1 1 2 3 −1 x −2 −1 1 2 x −2 −3 17. y 18. y 3 4 2 3 1 2 1 2 3 4 5 6 7 8 9 x 1 −4 −3 −2 −1 1 2 3 4 x 19. y 20. y 2 4 1 3 −4 −3 −2 −1 1 2 3 4 5 −1 x 2 1 −2 −3 −5 −4 −3 −2 −1 1 2 3 −1 −2 x 21. 9 8 7 6 5 4 3 2 1 y −3−2−1 1 2 3 x −1 −2 −3 −4 −5 22. y 5 4 3 2 1 −5−4−3−2−1 −1 1 2 3 4 5 −2 −3 −4 −5 x
1.3 Introduction to Functions 51 23. y 24. y 5 4 3 2 1 5 4 3 2 1 −5−4−3−2−1 −1 1 2 3 4 5 −2 −3 −4 −5 x −1 −1 1 2 3 4 5 6 −2 −3 −4 −5 x 25. y 26. y 4 4 3 3 2 2 1 1 −2 −1 1 2 x −2 −1 1 2 x 27. y 28. y 4 4 3 3 2 2 1 1 −2 −1 1 2 x −2 −1 1 2 x 29. y 30. y 2 2 1 1 −2 −1 1 2 −1 x −3 −2 −1 1 2 3 −1 x −2 −2
Page 1 and 2:
College Algebra Version ⌊π⌋ Co
Page 3 and 4:
Table of Contents Preface ix 1 Rela
Page 5 and 6:
Table of Contents v 4.3.3 Answers .
Page 7 and 8:
Preface Thank you for your interest
Page 9 and 10: xi text and we have gone to great l
Page 11 and 12: Chapter 1 Relations and Functions 1
Page 13 and 14: 1.1 Sets of Real Numbers and the Ca
Page 31 and 32: 1.2 Relations 21 Solution. 1. To gr
Page 33 and 34: 1.2 Relations 23 lines y = 1 and y
Page 35 and 36: 1.2 Relations 25 ‘connecting the
Page 37 and 38: 1.2 Relations 27 (x − 2) 2 + y 2
Page 39 and 40: 1.2 Relations 29 1.2.2 Exercises In
Page 41 and 42: 1.2 Relations 31 29. 5 4 3 y 30. 2
Page 43 and 44: 1.2 Relations 33 1.2.3 Answers 1. y
Page 45 and 46: 1.2 Relations 35 13. y 14. y 3 2
Page 47 and 48: 1.2 Relations 37 41. y = x 2 +1 The
Page 49 and 50: 1.2 Relations 39 45. y = √ x −
Page 51 and 52: 1.2 Relations 41 49. (x +2) 2 + y 2
Page 53 and 54: 1.3 Introduction to Functions 43 1.
Page 55 and 56: 1.3 Introduction to Functions 45 So
Page 57 and 58: 1.3 Introduction to Functions 47 Al
Page 59: 1.3 Introduction to Functions 49 1.
Page 63 and 64: 1.3 Introduction to Functions 53 1.
Page 65 and 66: 1.4 Function Notation 55 1.4 Functi
Page 67 and 68: 1.4 Function Notation 57 (c) To fin
Page 69 and 70: 1.4 Function Notation 59 1 − 4x x
Page 71 and 72: 1.4 Function Notation 61 these limi
Page 73 and 74: 1.4 Function Notation 63 1.4.2 Exer
Page 75 and 76: 1.4 Function Notation 65 ⎧ ⎪⎨
Page 77 and 78: 1.4 Function Notation 67 (b) How mu
Page 79 and 80: 1.4 Function Notation 69 1.4.3 Answ
Page 81 and 82: 1.4 Function Notation 71 18. For f(
Page 83 and 84: 1.4 Function Notation 73 26. For f(
Page 85 and 86: 1.4 Function Notation 75 69. C(0) =
Page 87 and 88: 1.5 Function Arithmetic 77 ( ) 4. F
Page 89 and 90: 1.5 Function Arithmetic 79 Next, we
Page 91 and 92: 1.5 Function Arithmetic 81 r(x + h)
Page 93 and 94: 1.5 Function Arithmetic 83 Solution
Page 95 and 96: 1.5 Function Arithmetic 85 27. f(x)
Page 97 and 98: 1.5 Function Arithmetic 87 1.5.2 An
Page 99 and 100: 1.5 Function Arithmetic 89 13. For
Page 101 and 102: 1.5 Function Arithmetic 91 37. 39.
Page 103 and 104: 1.6 Graphs of Functions 93 1.6 Grap
Page 105 and 106: 1.6 Graphs of Functions 95 In the p
Page 107 and 108: 1.6 Graphs of Functions 97 The calc
Page 109 and 110: 1.6 Graphs of Functions 99 The calc
Page 111 and 112:
1.6 Graphs of Functions 101 on [−
Page 113 and 114:
1.6 Graphs of Functions 103 1. Find
Page 115 and 116:
1.6 Graphs of Functions 105 Example
Page 117 and 118:
1.6 Graphs of Functions 107 1.6.2 E
Page 119 and 120:
1.6 Graphs of Functions 109 In Exer
Page 121 and 122:
1.6 Graphs of Functions 111 For Exe
Page 123 and 124:
1.6 Graphs of Functions 113 y y 4 5
Page 125 and 126:
1.6 Graphs of Functions 115 6. f(x)
Page 127 and 128:
1.6 Graphs of Functions 117 17. y 1
Page 129 and 130:
1.6 Graphs of Functions 119 90. h i
Page 131 and 132:
1.7 Transformations 121 7 y 7 y (5,
Page 133 and 134:
1.7 Transformations 123 2 to all of
Page 135 and 136:
1.7 Transformations 125 2 1 (0, 0)
Page 137 and 138:
1.7 Transformations 127 Solution. 1
Page 139 and 140:
1.7 Transformations 129 y y 3 2 1 (
Page 141 and 142:
1.7 Transformations 131 A few remar
Page 143 and 144:
1.7 Transformations 133 6 y 6 y (4,
Page 145 and 146:
1.7 Transformations 135 Finally, to
Page 147 and 148:
1.7 Transformations 137 (a, f(a)) a
Page 149 and 150:
1.7 Transformations 139 shift right
Page 151 and 152:
1.7 Transformations 141 Thecomplete
Page 153 and 154:
1.7 Transformations 143 64. The gra
Page 155 and 156:
1.7 Transformations 145 25. y =2−
Page 157 and 158:
1.7 Transformations 147 38. g(x) =f
Page 159 and 160:
1.7 Transformations 149 50. y = S 1
Page 161 and 162:
Chapter 2 Linear and Quadratic Func
Page 163 and 164:
2.1 Linear Functions 153 P 2 5. m =
Page 165 and 166:
2.1 Linear Functions 155 Equation 2
Page 167 and 168:
2.1 Linear Functions 157 y 4 3 2 y
Page 169 and 170:
2.1 Linear Functions 159 4. We find
Page 171 and 172:
2.1 Linear Functions 161 average sp
Page 173 and 174:
2.1 Linear Functions 163 2.1.1 Exer
Page 175 and 176:
2.1 Linear Functions 165 40. A rest
Page 177 and 178:
2.1 Linear Functions 167 61. y = 2
Page 179 and 180:
2.1 Linear Functions 169 2.1.2 Answ
Page 181 and 182:
2.1 Linear Functions 171 35. (a) F
Page 183 and 184:
2.2 Absolute Value Functions 173 2.
Page 185 and 186:
Page 187 and 188:
2.2 Absolute Value Functions 177 By
Page 189 and 190:
2.2 Absolute Value Functions 179 Ex
Page 191 and 192:
2.2 Absolute Value Functions 181 wh
Page 193 and 194:
Page 195 and 196:
2.2 Absolute Value Functions 185 24
Page 197 and 198:
2.2 Absolute Value Functions 187 31
Page 199 and 200:
2.3 Quadratic Functions 189 y y (
Page 201 and 202:
2.3 Quadratic Functions 191 shows t
Page 203 and 204:
2.3 Quadratic Functions 193 From g(
Page 205 and 206:
2.3 Quadratic Functions 195 ( a x +
Page 207 and 208:
2.3 Quadratic Functions 197 To find
Page 209 and 210:
2.3 Quadratic Functions 199 Neverth
Page 211 and 212:
2.3 Quadratic Functions 201 15. The
Page 213 and 214:
2.3 Quadratic Functions 203 2.3.2 A
Page 215 and 216:
2.3 Quadratic Functions 205 8. f(x)
Page 217 and 218:
2.3 Quadratic Functions 207 25. (a)
Page 219 and 220:
2.4 Inequalities with Absolute Valu
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
2.5 Regression 225 2.5 Regression W
Page 237 and 238:
2.5 Regression 227 2. Find the leas
Page 239 and 240:
2.5 Regression 229 The coefficient
Page 241 and 242:
2.5 Regression 231 4. The chart bel
Page 243 and 244:
2.5 Regression 233 2.5.2 Answers 1.
Page 245 and 246:
Chapter 3 Polynomial Functions 3.1
Page 247 and 248:
3.1 Graphs of Polynomials 237 of th
Page 249 and 250:
3.1 Graphs of Polynomials 239 In or
Page 251 and 252:
3.1 Graphs of Polynomials 241 Despi
Page 253 and 254:
3.1 Graphs of Polynomials 243 at th
Page 255 and 256:
3.1 Graphs of Polynomials 245 Theor
Page 257 and 258:
3.1 Graphs of Polynomials 247 In Ex
Page 259 and 260:
3.1 Graphs of Polynomials 249 37. T
Page 261 and 262:
3.1 Graphs of Polynomials 251 9. f(
Page 263 and 264:
3.1 Graphs of Polynomials 253 21. g
Page 265 and 266:
3.1 Graphs of Polynomials 255 33. (
Page 267 and 268:
3.2 The Factor Theorem and the Rema
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
3.3 Real Zeros of Polynomials 269 3
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
3.3 Real Zeros of Polynomials 275 f
Page 287 and 288:
3.3 Real Zeros of Polynomials 277 T
Page 289 and 290:
3.3 Real Zeros of Polynomials 279 (
Page 291 and 292:
3.3 Real Zeros of Polynomials 281 I
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
3.4 Complex Zeros and the Fundament
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
Page 309 and 310:
Page 311 and 312:
Chapter 4 Rational Functions 4.1 In
Page 313 and 314:
4.1 Introduction to Rational Functi
Page 315 and 316:
Page 317 and 318:
Page 319 and 320:
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
Page 329 and 330:
Page 331 and 332:
4.2 Graphs of Rational Functions 32
Page 333 and 334:
Page 335 and 336:
Page 337 and 338:
Page 339 and 340:
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
Page 349 and 350:
Page 351 and 352:
Page 353 and 354:
4.3 Rational Inequalities and Appli
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369 and 370:
Chapter 5 Further Topics in Functio
Page 371 and 372:
5.1 Function Composition 361 2. As
Page 373 and 374:
5.1 Function Composition 363 (+)
Page 375 and 376:
5.1 Function Composition 365 9. The
Page 377 and 378:
5.1 Function Composition 367 Theore
Page 379 and 380:
5.1 Function Composition 369 5.1.1
Page 381 and 382:
5.1 Function Composition 371 50. (g
Page 383 and 384:
5.1 Function Composition 373 7. For
Page 385 and 386:
5.1 Function Composition 375 20. Fo
Page 387 and 388:
5.1 Function Composition 377 56. (g
Page 389 and 390:
5.2 Inverse Functions 379 The main
Page 391 and 392:
5.2 Inverse Functions 381 y = f −
Page 393 and 394:
5.2 Inverse Functions 383 (b) We ca
Page 395 and 396:
5.2 Inverse Functions 385 y = f(x)
Page 397 and 398:
5.2 Inverse Functions 387 = = 2x 2x
Page 399 and 400:
5.2 Inverse Functions 389 We get g
Page 401 and 402:
5.2 Inverse Functions 391 Using wha
Page 403 and 404:
5.2 Inverse Functions 393 1. Explai
Page 405 and 406:
5.2 Inverse Functions 395 26. Show
Page 407 and 408:
5.3 Other Algebraic Functions 397 5
Page 409 and 410:
5.3 Other Algebraic Functions 399 I
Page 411 and 412:
5.3 Other Algebraic Functions 401 b
Page 413 and 414:
Page 415 and 416:
5.3 Other Algebraic Functions 405
Page 417 and 418:
Page 419 and 420:
Page 421 and 422:
Page 423 and 424:
Page 425 and 426:
5.3 Other Algebraic Functions 415 (
Page 427 and 428:
Chapter 6 Exponential and Logarithm
Page 429 and 430:
6.1 Introduction to Exponential and
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
Page 437 and 438:
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
Page 445 and 446:
Page 447 and 448:
6.2 Properties of Logarithms 437 6.
Page 449 and 450:
6.2 Properties of Logarithms 439 lo
Page 451 and 452:
6.2 Properties of Logarithms 441 ex
Page 453 and 454:
6.2 Properties of Logarithms 443 as
Page 455 and 456:
Page 457 and 458:
Page 459 and 460:
6.3 Exponential Equations and Inequ
Page 461 and 462:
Page 463 and 464:
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
6.4 Logarithmic Equations and Inequ
Page 471 and 472:
Page 473 and 474:
Page 475 and 476:
Page 477 and 478:
Page 479 and 480:
6.5 Applications of Exponential and
Page 481 and 482:
Page 483 and 484:
Page 485 and 486:
Page 487 and 488:
Page 489 and 490:
Page 491 and 492:
Page 493 and 494:
Page 495 and 496:
Page 497 and 498:
Page 499 and 500:
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
Chapter 7 Hooked on Conics 7.1 Intr
Page 507 and 508:
7.1 Introduction to Conics 497 If t
Page 509 and 510:
7.2 Circles 499 4 y 3 2 1 −4 −3
Page 511 and 512:
7.2 Circles 501 We close this secti
Page 513 and 514:
7.2 Circles 503 7.2.2 Answers 1. (x
Page 515 and 516:
7.3 Parabolas 505 7.3 Parabolas We
Page 517 and 518:
7.3 Parabolas 507 The distance from
Page 519 and 520:
7.3 Parabolas 509 Example 7.3.3. Gr
Page 521 and 522:
7.3 Parabolas 511 Every cross secti
Page 523 and 524:
7.3 Parabolas 513 7.3.2 Answers 1.
Page 525 and 526:
7.3 Parabolas 515 8. ( y + 2) 3 2 (
Page 527 and 528:
7.4 Ellipses 517 Minor Axis Major A
Page 529 and 530:
7.4 Ellipses 519 This equation is f
Page 531 and 532:
7.4 Ellipses 521 As with circles an
Page 533 and 534:
7.4 Ellipses 523 From this sketch,
Page 535 and 536:
7.4 Ellipses 525 7.4.1 Exercises In
Page 537 and 538:
7.4 Ellipses 527 7.4.2 Answers x 2
Page 539 and 540:
7.4 Ellipses 529 (x − 4) 2 (y −
Page 541 and 542:
7.5 Hyperbolas 531 7.5 Hyperbolas I
Page 543 and 544:
7.5 Hyperbolas 533 endpoints of the
Page 545 and 546:
7.5 Hyperbolas 535 from the center
Page 547 and 548:
7.5 Hyperbolas 537 As with the othe
Page 549 and 550:
7.5 Hyperbolas 539 y 6 5 4 3 2 Jeff
Page 551 and 552:
7.5 Hyperbolas 541 7.5.1 Exercises
Page 553 and 554:
7.5 Hyperbolas 543 is a hyperbola.
Page 555 and 556:
7.5 Hyperbolas 545 (y − 3) 2 (x
Page 557 and 558:
7.5 Hyperbolas 547 19. (x − 1) 2
Page 559 and 560:
Chapter 8 Systems of Equations and
Page 561 and 562:
8.1 Systems of Linear Equations: Ga
Page 563 and 564:
Page 565 and 566:
Page 567 and 568:
Page 569 and 570:
Page 571 and 572:
Page 573 and 574:
Page 575 and 576:
Page 577 and 578:
8.2 Systems of Linear Equations: Au
Page 579 and 580:
Page 581 and 582:
Page 583 and 584:
Page 585 and 586:
Page 587 and 588:
Page 589 and 590:
8.3 Matrix Arithmetic 579 ⎡ ⎤
Page 591 and 592:
8.3 Matrix Arithmetic 581 As did ma
Page 593 and 594:
8.3 Matrix Arithmetic 583 While the
Page 595 and 596:
8.3 Matrix Arithmetic 585 Using Ri
Page 597 and 598:
8.3 Matrix Arithmetic 587 C 2 − 5
Page 599 and 600:
8.3 Matrix Arithmetic 589 ( √2 2
Page 601 and 602:
8.3 Matrix Arithmetic 591 8.3.1 Exe
Page 603 and 604:
8.3 Matrix Arithmetic 593 28. Now l
Page 605 and 606:
8.3 Matrix Arithmetic 595 8.3.2 Ans
Page 607 and 608:
8.3 Matrix Arithmetic 597 [ ] −9
Page 609 and 610:
8.4 Systems of Linear Equations: Ma
Page 611 and 612:
Page 613 and 614:
Page 615 and 616:
Page 617 and 618:
Page 619 and 620:
Page 621 and 622:
Page 623 and 624:
Page 625 and 626:
8.5 Determinants and Cramer’s Rul
Page 627 and 628:
Page 629 and 630:
Page 631 and 632:
Page 633 and 634:
Page 635 and 636:
Page 637 and 638:
Page 639 and 640:
8.6 Partial Fraction Decomposition
Page 641 and 642:
Page 643 and 644:
Page 645 and 646:
Page 647 and 648:
8.7 Systems of Non-Linear Equations
Page 649 and 650:
Page 651 and 652:
Page 653 and 654:
Page 655 and 656:
Page 657 and 658:
20. Solve the following system ⎧
Page 659 and 660:
Page 661 and 662:
Chapter 9 Sequences and the Binomia
Page 663 and 664:
9.1 Sequences 653 3. From {2n − 1
Page 665 and 666:
9.1 Sequences 655 Solution. A good
Page 667 and 668:
9.1 Sequences 657 Looking at the de
Page 669 and 670:
9.1 Sequences 659 28. 0.9, 0.99, 0.
Page 671 and 672:
9.2 Summation Notation 661 9.2 Summ
Page 673 and 674:
9.2 Summation Notation 663 5∑ (
Page 675 and 676:
9.2 Summation Notation 665 S = n (2
Page 677 and 678:
9.2 Summation Notation 667 payment
Page 679 and 680:
9.2 Summation Notation 669 n∑ k=1
Page 681 and 682:
9.2 Summation Notation 671 In Exerc
Page 683 and 684:
9.3 Mathematical Induction 673 9.3
Page 685 and 686:
9.3 Mathematical Induction 675 This
Page 687 and 688:
9.3 Mathematical Induction 677 it i
Page 689 and 690:
9.3 Mathematical Induction 679 9.3.
Page 691 and 692:
9.4 The Binomial Theorem 681 9.4 Th
Page 693 and 694:
9.4 The Binomial Theorem 683 songs
Page 695 and 696:
9.4 The Binomial Theorem 685 (a + b
Page 697 and 698:
9.4 The Binomial Theorem 687 ∑k
Page 699 and 700:
9.4 The Binomial Theorem 689 ( 0 0)
Page 701 and 702:
9.4 The Binomial Theorem 691 9.4.1
Page 703 and 704:
Index n th root of a complex number
Page 705 and 706:
Index 1071 central angle, 701 chang
Page 707 and 708:
Index 1073 reflective property, 523
Page 709 and 710:
Index 1075 matrix, multiplicative,
Page 711 and 712:
Index 1077 midpoint definition of,
Page 713 and 714:
Index 1079 instantaneous, 161, 472
Page 715 and 716:
Index 1081 inconsistent, 553 indepe
show all

College Algebra, 2013a

Create successful ePaper yourself

Delete template?

Save as template?