Find the Domain and Range for Each of the Following

Domain and Range Class Work Find the domain and range for each of the following 1. {(1,2), (3,4), (5,6)} 2. {(4,3), (3,2), (4,2)} 3. {(5,1), (3,1), (-4,1)}

4. 5. 6.

7. 8. 9.

10. 11. 12. 13.

Homework Find the domain and range for each of the following 14. {(3,1), (-2,6), (1,4)} 15. {(1,2), (2,2), (1,2)} 16. {(2,1), (5,1), (-6,7)}

17. 18. 19.

20. 21. 22. 23. 24.

25. 26.

Discrete vs. Continuous Class Work Is the relation discrete or continuous? 47. {(1,2), (3,4), (5,6)} 48. {(4,3), (3,2), (4,2)} 49. {(5,1), (3,1), (-4,1)}

50. 51. 52.

53. 54. 55.

56. 57.

58. 59.

Homework Is the relation discrete or continuous? 60. {(3,1), (-2,6), (1,4)} 61. {(1,2), (2,2), (1,2)} 62. {(2,1), (5,1), (-6,7)}

63. 64. 65.

66. 67. 68.

69. 70.

71. 72.

Relations and Functions Class Work Is the relation a function? 73. {(1,2), (3,4), (5,6)} 74. {(4,3), (3,2), (4,2)} 75. {(5,1), (3,1), (-4,1)} 76. 77. 78.

79. 80. 81.

82. 83.

84. 85.

Homework Is the relation a function? 86. {(3,1), (-2,6), (1,4)} 87. {(1,2), (2,2), (1,2)} 88. {(2,1), (5,1), (-6,7)}

89. 90. 91.

92. 93. 94.

95. 96.

97. 98.

Evaluating Functions Class Work Let f(x)= 3x+4 and g(x)= |x-4|, find the following 99. f(2) 100. f(3) 101. g(6) 102. g(2) 103. 2f(6) 104. .5g(2) 105. f(4) – g(3) 106. g(5) – f(5) 107. f(0)2 108. g(3)3 109. g(a) 110. f(2b)

Class Work Let f(x)= (x-1)2 and g(x)= |2x-3|, find the following 111. f(2) 112. f(3) 113. g(6) 114. g(2) 115. 2f(6) 116. .5g(2) 117. f(4) – g(3) 118. g(5) – f(5) 119. f(0)2 120. g(3)3 121. g(a) 122. f(2b)

Graphing Linear Equations Chapter Problems

Graph using a table

Classwork

For the equations below, make a table with at least 3 ordered pairs, plot the points and connect them to form the line.

123. y = 3x – 4 124. y = -2x + 4

125. y = x – 3

126. y = x + 4

127. y = - x + 1

Homework

For the equations below, make a table with at least 3 ordered pairs, plot the points and connect them to form the line.

128. y = -x – 2

129. y = 2x + 1 130. y = x

131. y = -2x – 2

132. y = - x + 4

Graph using the slope and y-intercept

Classwork

133. Use lines A, B, C and D to answers the questions.

a. What is the y-intercept of each line?

b. Is the slope of each line positive, negative, zero or undefined?

134. What is the slope of lines E, F, G and H?

135. What are the equations of lines E, F ,G and H?

Homework

136. Use lines I, J, K and L to answers the questions.

a. What is the y-intercept of each line?

b. Is the slope of each line positive, negative, zero or undefined?

137. What are the slopes of lines M, N, O and P? 138. What is the equation of lines M, N, O and P?

Graph using intercepts

Classwork

Rewrite the equations in standard form. Graph the intercepts and then the line that passes through them.

139. y = 3x + 4

140. y = -2x + 3

141. y = x + 7

142. y = x – 2

143. y = - 3x

144. y = - x + 5

145. y – 4 = 2(x – 5)

146. y + 5 = -3(x – 4)

147. y + 6 = (x – 6)

148. y – 3 = (x + 7)

Homework

Rewrite the equations in standard form. Graph the intercepts and then the line that passes through them.

149. y = 6x + 4

150. y = -3x – 2

151. y = x – 3

152. y = x + 4

153. y = - x – 2

154. y = -7x

155. y – 5 = 2(x – 3)

156. y + 2 = -4(x – 2)

157. y – 3 = (x – 3)

158. y + 1 = 2(x + 1)

Horizontal & Vertical Lines Classwork

Determine if the following equations are horizontal, vertical, neither or cannot be determined.

159. y = -5

160. x = 7

161. 2x + 4y = 8

162. 7x – 21 = 0

163. 3x + 2y = 3x – 4

Homework

Determine if the following equations are horizontal, vertical, neither or cannot be determined.

164. x = -5

165. y = 7

166. 8x + -4y = -2

167. -6x – 3y = -6x + 2

168. -8x = -24

Slope Formula

Classwork

Find the slope of the line through each of the following two points.

169. (-12,-5), (0,-8)

170. (12,-18),(11,12)

171. (-18,-20),(-18,-15)

172. (-20,-4),(-12,-10)

173. (8,10),(0,14)

174. (6,9),(3,-9)

175. (1,2),(5,7)

176. (3,-3),(12,-2)

177. (-4,-8),(-1,1)

178. (4,7),(-3,7)

Homework Find the slope of the line through each of the following two points.

179. (3,-9),(1,1)

180. (7,4),(3,8)

181. (-3,0),(5,12)

182. (8,-2),(12,-2)

183. (6,-3),(2,9)

184. (-3,7),(-4,8)

185. (5,9),(5,-8)

186. (-5, 0.5),(-6,3)

187. (-7,1),(7,8)

188. (-2,1),(5,7)

Parallel and Perpendicular Lines

Classwork

Match the following parallel equations from each column.

189. y = 3x – 2 194. 3y = x + 18

190. y = -2x + 1 195. -4x + 17 = 2y

191. y = x – 7 196. 7y – 6x = 0

192. 6x – 2 = 7y 197. -5(3y – 9x) = 30

193. 2(y + x) = 18 198. 14y = 12x + 28

199. Match the following perpendicular equations from each column.

200. y = -4x – 4 205. y + 3 = -2(x – 5)

201. 2y = 3x + 12 206. 4y = x – 4

202. 7x + y = -10 207. 2x = 14y -8

203. y – 5 = (x + 4) 208. y + 4 = (x – 4)

204. 3(4y + 8x) = 0 209. 2x + 3y = 15

211. Write an equation that would be parallel to the line y = 4x + 7 212.

213. Write an equation that would be perpendicular to the line 4x + 6y = -12

218. Homework

219. Match the following parallel equations from each column.

220. y = 3x+ 7 225. 24x – 6y = 18 221. 4y = 16x + 12 226. y + 5 = 2(x – 13) 222. 6x + 12y = 1 227. 2y + x = 24 223. y – 4 = (x – 11) 228. 3(15y – 12x) = 27 224. 0 = 22x – 11y 229. -12x = -4y – 16 230. Match the following perpendicular equations from each column.

231. 6y = -12x + 9 236. y – 9 = -4(x – 2)

232. y – 4 = (x + 7) 237. 3x + 21y = 0

233. 5(2x – 8y) = 35 238. 8(14y – 7x) = 24

234. 35x – 5y = 0 239. y = -5x + 5

235. 19 + y = -3x 240. -10x + 30y + 20 = 0

241. 242. Write an equation that would be parallel to the line 6y = -24y – 18

244. Write an equation that would be perpendicular to the line y – 4 = (x + 4)

245. Graph using point slope

246. Classwork

247. Graph each equation

248. y – 2 = (x – 3)

249. y + 5 = 2(x + 2)

250. y – 4 = -3(x – 3)

251. y + 7 = (x – 1) 252. y – 3 = - (x + 5)

253. Homework

254. Graph each equation

255. y – 2 = (x + 4)

256. y + 5 = -2(x – 4)

257. y – 1 = 4(x – 2)

258. y – 5 = - (x – 1)

259. y – 0 = (x – 3)

261. How to write equations from given information

262. Classwork

263. Write an equation in point slope form for the line through the given point with the given slope.

a. (3,4); m = 6

b. (-2,-7); m = -

c. (7,-4); m = -3

d. (4,0); m = 1

e. (-4,-4); m =

265. A line passes through the given points. First write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form.

a. (-1,0), (1,2)

b. (3,5), (0,0)

c. (6,-2), (9,-8)

d. (-1,-5), (-7,-6)

e. (-3,4), (3,-2)

267. Write the equation of the line through the given points in standard form.

a. (6,3), (-4, 2) b. (12,3), (-8,-4)

c. (15,-4), (8, -3)

d. (7,2), (8,5)

e. (20,-10), (-30, 0)

269. A line has an x-intercept of 8 and y-intercept of 12.

a. Write an equation for the line.

b. Write an equation that is parallel to this line.

c. Write an equation that is perpendicular to the line from part a.

271. Write the equation of the line through (-3,-2) and is parallel to the line y = -2x + 5

273. Write the equation of the line through (7,4) and perpendicular to y = x – 5

274. Homework

275. Write an equation in point slope form for the line through the given point with the given slope.

a. (5,-4); m = -2

b. (-2, -3); m = 4

c. (7,4); m =

d. (9,-9); m = 3

e. (6,0); m = -

276. A line passes through the given points. First write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form.

a. (-10,-50), (5,25)

b. (0,10), (10,-20)

c. (0.5,9), (50,-90)

d. (8,9), (5,-6)

e. (-7, 4), (-3,6)

277. 278. Write the equation of the line through the given points in standard form.

a. (1,4), (-1,1)

b. (5,-3), (3,4)

c. (2,4), (-3,-6)

d. (5,3), (4,5)

e. (0,0), (-1,-2)

280. A line has an x-intercept of -4 and y-intercept of 16.

a. Write an equation for the line.

b. Write an equation that is parallel to this line.

c. Write an equation that is perpendicular to the line from part a.

282. Write the equation of the line through (8,5) and is parallel to the line y = x + 7

284. Write the equation of the line through (-2,5) and perpendicular to y = - x + 3

285. Scatter Plots and Lines of Best Fit 286. Classwork 287. 255. Predict the test score of someone who spends 48 minutes studying.

110 105 100 95 s

e 90 r o

c 85 s

s 80 e t 75 70 65 60 25 30 35 40 45 50 55 60 Tim e spent studying

289. 256 Predict the test score of someone who spends 34 minutes studying. 110 105 100 95 s

e 90 r o

c 85 s

s 80 e t 75 70 65 60 25 30 35 40 45 50 55 60 Tim e spent studying

291. 257. Draw a scatter plot from the following data:

292. Size of shoe Height (inches)

5 55 5.5 58 6 62 7 68 293. 6.5 63 294. 7.3 70 295. 8 79 296. 8.7 88 297. 258. Consider the scatter graph to answer the following:

298. Which two points would give the line of best fit?

299. A and B

300. A and C

301. D and B

302. There is no pattern

304. 259.Consider the scatter graph to answer the following:

305. Which two points would give the line of best fit?

306. A and B

307. B and C

308. C and D

309. There is no pattern

310. Homework 311. 260. Using the scatter graph, predict the mile time of someone who spends 6 hours a week training.

e 9:31 m i t

M 8:19

5:55 0 5 10 15 20 25 Time spent training

314. 261. Using the scatter graph, predict the mile time of someone who spends 12 hours a week

e 9:31 m i t

M 8:19

5:55 0 5 10 15 20 25 Time spent training

training.

317. 262. Draw a scatter graph from the following data,

318. Time spent studying (min) Grade

55 97 31 78 52 90 20 61 42 84 47 90 31 81 319.

320. 263. Consider the scatter graph to answer the following: 321. Which point would most likely be on the line best fit? 322. A 323. B 324. C 325. There would be no line of best fit 326.

330. 264. Consider the scatter graph to answer the following: 331. Which two points would give the line of best fit? 332. A and D 333. A and C 334. B and D 335. There is no pattern 336.

339. Determining the Prediction Equation

341. Class Work

342. 265. Use the two points (7,14) and (15,27)

343. to write an equation for the line of best fit. 344.

345. 266. If the prediction equation is y=.5t+60, where

346. t represents time in minutes, what will the person get on his test if he studies for 45 minutes?

348. 267. If the prediction equation to determine a test grade is y=.5t+60, and someone received an 80 on the test, how long did they study for?

349. 350. Consider the scatter graph to answer 268-270:10 351. 9 352. 268. What is the slope of the line of best fit that8 7 353. passes through (3.4, 7) and (8, 3)? 6

354. 5 355. 269. What is the y-intercept of the line of best fit4 that 356. passes through (3.4, 7) and (8, 3)? 3 2

357. 1 358. 270. Consider the scatter graph to answer the 0 0 1 2 3 4 5 6 7 8 9 10 359. following: The equation for the line of best fit is 360. y = -1.06x + 10.7. Determine the value for x=15? 361. Is this an interpolation or extrapolation? 362. 363. 10 364. Homework 9 2, 9.2 8 3, 8.1 365. 271. Using the scatter graph below use the two7 3.4, 7 6 4, 5.4 366. points (3.4, 7) and (9, 1) to write an equation5 for

4 5.3, 4.2 367. the line of best fit. 7.5, 3.7 368. 3 2

1 9, 1 369. 0 0 1 2 3 4 5 6 7 8 9 10 370.

371. 272. If the prediction equation for a test grade is y=.52t+65, where t represents the time in minutes, what grade will someone earn if they study for 30 minutes.

373. 273. If the prediction equation for a test grade is y=.52t+65, where t represents the time in minutes, how long did someone study for if they received an 83 on the exam?

375. Consider the scatter graph to answer 274-276:

376. 274. What is the slope of the line of best fit passing

377. through (2.7, 11.1) and (9.4, 3.7)?

379. 275. What is the y-intercept of the line of best fit

380. passing through (2.7, 11.1) and (9.4, 3.7)?

382. 383. 276. Consider the scatter graph. The equation for the line of best fit is y= -.98x+13.6. Determine the value for x=5. Is this an interpolation or extrapolation? 384. 385. Absolute Value Functions 386. Class Work 387. On a separate sheet of paper, graph the following. Sate the domain and range of each. 277. y = |x| 278. y =|x + 3| 279. y = |x – 2| 280. y = |x + 4| 281. y = |x – 3| 282. y = |x| + 3 283. y = |x| - 2 284. y = |x| + 4 285. y = |x| - 3 286. y = |x - 6| - 2 287. y = |x + 4| +3 288. y =-|x| 289. y= 3|x| 290. y = -2|x+4| +3 291. y = .5|x – 6| -2 388. 389. Homework 390. On a separate sheet of paper, graph the following. Sate the domain and range of each. 292. y =|x - 3| 293. y = |x + 2| 294. y = |x - 4| 295. y = |x + 3| 296. y = |x| - 3 297. y = |x| + 2 298. y = |x| - 4 299. y = |x| + 3 300. y = |x + 6| + 2 301. y = |x - 4| - 3 302. y =|-x| 303. y= -3|x| 304. y = 2|x - 4| - 3 305. y = -.5|x + 6| + 2 391. 392. Greatest Integer Function 393. Class Work 394. Evaluate the following. 306. [2.2] 307. [3.5] 308. [5.9] 309. [7.98] 310. [8] 311. [-3.9] 312. [-3.4] 313. [0] 314. [3.2 +4.5] 315. [6.1 – 6.7] 395. 396. On a separate sheet of paper graph 397. 316. y = [x + 1] 398. 317. f(x)= 2[x] 399. 318. g(x)=-[x] 400. 319. h(x)= [x] -3 401. 402. 403. Homework 404. Evaluate the following. 320. [3.4] 321. [3.8] 322. [7.95] 323. [9.98] 324. [10] 325. [-3.8] 326. [-2.3] 327. [0.1] 328. [3(2.1)] 329. [-2(4.2)] 405. 406. On a separate sheet of paper graph 407. 330. y = [x - 1] 408. 331. f(x)= 3[x] 409. 332. g(x)=[-x] 410. 333. h(x)= [x] + 3 411. 412. Piecewise Functions 413. Class Work 414. 334. 415. 416. 417. 418. a. f(-2) 419. b. f(0) 420. c. f(4) 421. d. state the domain and range of f 422. e. graph f 423. 424. 335. 425. 426. 427. 428. a. f(-2) 429. b. f(2) 430. c. f(4) 431. d. state the domain and range of f 432. e. graph f 433. 336. 434. 435. 436. 437. a. f(-2) 438. b. f(1) 439. c. f(4) 440. d. state the domain and range of f 441. e. graph f 442. 443. 337. 444. 445. 446. 447. a. f(-2) 448. b. f(0) 449. c. f(4) 450. d. state the domain and range of f 451. e. graph f 452. 338. 453. 454. 455. 456. a. f(-2) 457. b. f(2) 458. c. f(4) 459. d. state the domain and range of f 460. e. graph 461. Homework 462. 463. 339. 464. 465. 466. 467. a. f(-2) 468. b. f(0) 469. c. f(4) 470. d. state the domain and range of f 471. e. graph f 472. 473. 340. 474. 475. 476. 477. a. f(-2) 478. b. f(2) 479. c. f(4) 480. d. state the domain and range of f 481. e. graph f 482. 341. 483. 484. 485. 486. a. f(-2) 487. b. f(1) 488. c. f(4) 489. d. state the domain and range of f 490. e. graph f 491. 492. 342. 493. 494. 495. 496. a. f(-2) 497. b. f(0) 498. c. f(4) 499. d. state the domain and range of f 500. e. graph f 501. 343. 502. 503. 504. 505. a. f(-2) 506. b. f(2) 507. c. f(4) 508. d. state the domain and range of f 509. e. graph 510. Graphing Linear Inequalities 511. Class Work 512. Graph the following inequalities 513. 344. 514. 345. 515. 346. 516. 347. 517. 348. 518. 349. 519. 520. Write the equation for the inequality graphed. 521. 350. 351. 522. 523. 524. 525. 526. 527. 528. 529. 530. 531. 532. 533. 534. Class Work 535. Graph the following inequalities 536. 352. 537. 353. 538. 354. 539. 355. 540. 356. 541. 357. 542. 543. Write the equation for the inequality graphed. 544. 358. 359. 545. 546. 547. 548. 549. 550. 551. 552. 553. 554. 555. 556. Linear Relations- Multiple Choice 557. 1. Find the domain of {(1,3), (5,6), (6,8)} 558. A. {1, 5, 8} 559. B. {1, 5, 6} 560. C. {3, 6, 8} 561. D. Set of Reals 562. 563. 2. Find the range of f(x)= |x - 2| +3 564. A. [3, ∞] 565. B. [1, ∞) 566. C.(1, ∞) 567. D. [3, ∞) 568. 569. 3. What is domain of the following graph? 570. A. {x| -10< x< 10} 571. B. {x| -10< x< 10} 572. C. {x| -6< x< -2 or 0< x< 6} 573. D. {x| -10< x< -4 or -2< x< 4 or 6< x< 10} 574. 575. 4. Which choice represents a discrete set? 576. A. the time it takes people to tie their shoes 577. B. amount of rain in a given week 578. C. number of people attending a play 579. D. the number of rotations of a wheel 580. 581. 5. Which of the following is a function? 582. A. x2 + y2 = 4 583. B. x + y2 = 4 584. C. x2 + y = 4 585. D. 4x2 + y2 = 4 586. 587. 6. Given f(x) = 2(x-6)2 +2, find f(3) 588. A. 2 589. B. 20 590. C. 29 591. D. 38 592. 593. 7. The x-intercept of 4x + 3y = 12 is 594. A. 4 595. B. (4,0) 596. C. 3 597. D. (3,0) 598. 599. 8. The slope of 4x + 3y = 12 is 600. A. 4 601. B. -4 602. C. 603. D. 604. 605. 606. 60 60 7. 8. X Y 60 61 9. 0. 0 3 61 61 1. 2. 2 5 61 61 3. 4. 3 7 615. 9. The equation of the line containing the points in the table is 616. A. y= x + 3 617. B. y= 2x + 3 618. C. y= x + 3 619. D. Points in table are not collinear 620. 621. 10. A line parallel to y = 2x + 6 is 622. A. y= 2x -1 623. B. y-4 = 2(x+3) 624. C. 10x – 5y = 7 625. D. All of the above 626. 627. 11. The slope of a line perpendicular to the line thru (3,6) and (5,2) is 628. A. -2 629. B. 630. C. 631. D. 2 632. 633. 12. An example of a line with no slope is 634. A. y = x 635. B. y = 3 636. C. x = 2 637. D. y = 0 – x 638. 639. 13. A line thru (3,-2) and (4,6) has equation 640. A. y – 6 = 8(x – 4) 641. B. y – 6 = 4(x – 4) 642. C. y + 2 = 8(x + 3) 643. D. Both A and C 644. 645. 14. The equation of a line perpendicular to f(x) is 646. A. y= -2x +4 647. B. y= 2x + 5 648. C. y= x – 3 649. D. y= x 650. 651. 15. Using the graph of f(x), find f(6). 652. A. -1 653. B. -2 654. C. -3 655. D. Undefined 656. 657. 658. 659. 660. 661. 662. In 16 and 17, consider the piecewise function 663. 16. Find g(3) 664. A. -9 665. B. 1 666. C. -9 or 1 667. D. Does not exist 668. 669. 17. The slope at x=1 is 670. A. -3 671. B. -1 672. C. 1 673. D. 0 674. 675. 18. Find [3.75] 676. A. 3 677. B. 3.7 678. C. 3.8 679. D. 4 680. 681. 19. Find [-4.14] 682. A. -5 683. B. -4.2 684. C. -4.1 685. D. -4 686. 687. 20. When graphing y > 2x -3 688. A. solid boundary and shade above 689. B. dotted boundary and shade above 690. C. solid boundary and shade below 691. D. dotted boundary and shade below 692. 693. 21. Which point could be used as a test point to decide where to shade when graphing y > 4x? 694. A. (0 ,0) 695. B. (-2 ,-8) 696. C. ( 3 , 10) 697. D. both B and C 698. 699. Extended Response 700. 1. An employer offers $12 an hour for the first eight hours of work and 1.5 times that rate for overtime. 701. a. Create a piecewise function that models this situation. 702. b. Make a graph of the equation in part A (Let the domain be [0,15]) 703. c. How much does a person make if they work 10 hours? 704. d. If a raise of $2 was given, describe how the piecewise function would change. 705. 706. 2. Cal C.’s grandmother offers him $5 for every A he receives on his report card. 707. a. If he takes 8 classes, what are the domain and range? 708. b. Is the answer in part A discrete or continuous? Is it a function? 709. c. If his grandfather gives him $10 for finishing the marking period, write an equation for how much he can make with one report card. 710. 3. Line segment connects A(4,2) and B(7,6). 711. a. What is the slope of ? 712. b. is the side of a rectangle, what are the slopes of the other three sides. 713. c. Write the equation of . 714. 715. 4. Given y - 3 = (x – 8) 716. a. Write the equation in slope y-intercept form 717. b. Write the equation in standard form 718. c. The line is rotated about the point (8,3), what is the equation of the new line? 719. 720. Answers 1) D:{1,3,5} R:{2,4,6} 4) D:{-3,1,2} R:{2,5,7} 2) D:{3,4} R:{2,3} 5) D:{4,5,6} R:{6} 3) D:{-4, 3,5} R:{1} 6) D:{-4,0,2} R:{3,4,5} 7) D:{-2,-1,2,3} R:{0,3,4,5,7} 78) no 8) D:{1,2} R:{3,4,5,6} 79) no 9) D:{-4,0,1,2,3} R:{5,6,7} 80) no 10) D:{-4,-2,1,3} R:{0,3,4,5,7} 81) yes 11) D:{x>-4} R:{y>0} 82) no 12) D:{x<-2 or x>2} R:{Reals} 83) yes 13) D:{Reals} R:{Reals} 84) yes 14) D:{-2,1,3} R:{1,4,6} 85) yes 15) D:{1,2} R:{2} 86) yes 16) D:{-6,2,5} R:{1,7} 87) no 17) D:{-1,0,1} R:{6,7,8} 88) yes 18) D:{2,4} R:{6,7,8} 89) yes 19) D:{-5,0,5} R:{-2,-1,0} 90) no 20) D:{3,4,5,6} R:{1,2,3,4} 91) no 21) D:{5} R:{0,1,2,3} 92) yes 22) D:{3,4} R:{2,3,4} 93) no 23) D:{-4,-2,2,4,5} R:{-3,2,4,5} 94) no 24) D:{-6