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All Textbook Solutions for Intermediate Algebra
In the following exercises, use the mapping of the relation to (a) list the ordered pairs of the relation, (b) find the domain of the relation, and (c) find the range of the relation. 287.In the following exercises, use the mapping of the relation to (a) list the ordered pairs of the relation, (b) find the domain of the relation, and (c) find the range of the relation. 288.In the following exercises, use the mapping of the relation to (a) list the ordered pairs of the relation, (b) find the domain of the relation, and (c) find the range of the relation. 289. For a woman of height 5'4 " the mapping below shows the corresponding Body Mass Index (BMI). The body mass index is a measurement of body fat based on height and weight. A BMI of 18.524.9 is considered healthy.In the following exercises, use the mapping of the relation to (a) list the ordered pairs of the relation, (b) find the domain of the relation, and (c) find the range of the relation. 290. For a man of height 5'11'' the mapping below shows the corresponding Body Mass Index (BMI). The body mass index is a measurement of body fat based on height and weight. A BMI of 18.524.9 is considered healthy.In the following exercises, use the graph of the relation to (a) list the ordered pairs of the relation (b) find the domain of the relation (c) find the range of the relation. 291.In the following exercises, use the graph of the relation to (a) list the ordered pairs of the relation (b) find the domain of the relation (c) find the range of the relation. 292.In the following exercises, use the graph of the relation to (a) list the ordered pairs of the relation (b) find the domain of the relation (c) find the range of the relation. 293.In the following exercises, use the graph of the relation to (a) list the ordered pairs of the relation (b) find the domain of the relation (c) find the range of the relation. 294.In the following exercises, use the set of ordered pairs to (a) determine whether the relation is a function, (b) find the domain of the relation, and (c) find the range of the relation. 295. {(3,9),(2,4),(1,1),(0,0),(1,1),(2,4),(3,9)}In the following exercises, use the set of ordered pairs to (a) determine whether the relation is a function, (b) find the domain of the relation, and (c) find the range of the relation. 296. {(9,3),(4,2),(1,1),(0,0),(1,1),(4,2),(9,3)}In the following exercises, use the set of ordered pairs to (a) determine whether the relation is a function, (b) find the domain of the relation, and (c) find the range of the relation. 297. {(3,27),(2,8),(1,1)(0,0),(1,1),(2,8),(3,27)}In the following exercises, use the set of ordered pairs to (a) determine whether the relation is a function, (b) find the domain of the relation, and (c) find the range of the relation. 298. {(9,3),(4,2),(1,1),(0,0),(1,1),(4,2),(9,3)}In the following exercises, use the mapping to (a) determine whether the relation is a function, (b) find the domain of the function, and (c) find the range of the function. 299.In the following exercises, use the mapping to (a) determine whether the relation is a function, (b) find the domain of the function, and (c) find the range of the function. 300.In the following exercises, use the mapping to (a) determine whether the relation is a function, (b) find the domain of the function, and (c) find the range of the function. 301.In the following exercises, use the mapping to (a) determine whether the relation is a function, (b) find the domain of the function, and (c) find the range of the function. 302.In the following exercises, determine whether each equation is a function. 303. (a) 2x+y=3 (b) y=x2 (c) x+y2=5In the following exercises, determine whether each equation is a function. 304. (a) y=3x5 (b) y=x3 (c) 2x+y2=4In the following exercises, determine whether each equation is a function. 305. (a) y3x3=2 (b) x+y2=3 (c) 3x2y=6In the following exercises, determine whether each equation is a function. 306. (a) 2x4y=8 (b) 4=x2y (c) y2=x+5In the following exercises, evaluate the function: (a) f(2)(b) f(1)(c) f(a). 307. f(x)=5x3In the following exercises, evaluate the function: (a) f(2)(b) f(1)(c) f(a). 308. f(x)=3x+4In the following exercises, evaluate the function: (a) f(2)(b) f(1)(c) f(a). 309. f(x)=4x+2In the following exercises, evaluate the function: (a) f(2)(b) f(1)(c) f(a). 310. f(x)=6x3In the following exercises, evaluate the function: (a) f(2)(b) f(1)(c) f(a). 311. f(x)=x2x+3In the following exercises, evaluate the function: (a) f(2)(b) f(1)(c) f(a). 312. f(x)=x2+x2In the following exercises, evaluate the function: (a) f(2)(b) f(1)(c) f(a). 313. f(x)=2x2x+3In the following exercises, evaluate the function: (a) f(2)(b) f(1)(c) f(a). 314. f(x)=3x2+x2In the following exercises, evaluate the function: (a) g(h2)(b) g(x+2)(c) g(x)+g(2). 315. g(x)=2x+1In the following exercises, evaluate the function: (a) g(h2)(b) g(x+2)(c) g(x)+g(2). 316. g(x)=5x8In the following exercises, evaluate the function: (a) g(h2)(b) g(x+2)(c) g(x)+g(2). 317. g(x)=3x2In the following exercises, evaluate the function: (a) g(h2)(b) g(x+2)(c) g(x)+g(2). 318. g(x)=8x+2In the following exercises, evaluate the function: (a) g(h2)(b) g(x+2)(c) g(x)+g(2). 319. g(x)=3x?y13In the following exercises, evaluate the function: (a) g(h2)(b) g(x+2)(c) g(x)+g(2). 320. g(x)=75xIn the following exercises, evaluate the function. 321. f(x)=3x25x;f(2)In the following exercises, evaluate the function. 322. g(x)=4x23x;g(3)In the following exercises, evaluate the function. 323. F(x)=2x23x+1;F(1)In the following exercises, evaluate the function. 324. G(x)=3x25x+2;G(2)In the following exercises, evaluate the function. 325. h(t)=2|t5|+4;f(4)In the following exercises, evaluate the function. 326. h(y)=3|y1|3;h(4)In the following exercises, evaluate the function. 327. f(x)=x+2x1;f(2)In the following exercises, evaluate the function. 328. g(x)=x2x+2;g(4)In the following exercises, solve. 329. The number of unwatched shows in Sylvia’s DVR is 85. This number grows by 20 unwatched shows per week. The function N(t)=85+20t represents the relation between the number of unwatched shows, N, and the time, t, measured in weeks. (a) Determine the independent and dependent variable. (b) Find N(4) . Explain what this result meansIn the following exercises, solve. 330. Every day a new puzzle is downloaded into Ken’s account. Right now he has 43 puzzles in his account. The function N(t)=43+t represents the relation between the number of puzzles, N, and the time, t, measured in days. (a) Determine the independent and dependent variable. (b) Find N(30) . Explain what this result means.In the following exercises, solve. 331. The daily cost to the printing company to print a book is modeled by the function C(x)=3.25x+1500 where C is the total daily cost and x is the number of books printed. (a) Determine the independent and dependent variable. (b) Find N(0) . Explain what this result means. (c) Find N(1000) . Explain what this result means.In the following exercises, solve. 332. The daily cost to the manufacturing company is modeled by the function C(x)=7.25x+2500 where C(x) is the total daily cost and x is the number of items manufactured. (a) Determine the independent and dependent variable. (b) Find C(0) . Explain what this result means. (c) Find C(1000) . Explain what this result means.In your own words, explain the difference betweena relation and a function.In your own words, explain what is meant by domain and range.Is every relation a function? Is every function a relation?How do you find the value of a function?Determine whether each graph is the graph of a function.Determine whether each graph is the graph of a function.Graph: f(x)=3x1Graph: f(x)=4x5Graph: f(x)=2Graph: f(x)=3 .Graph: f(x)=x2 .Graph: f(x)=x2Graph: f(x)=x3 .Graph: f(x)=x3 .Graph: f(x)=x .Graph: f(x)=x .Graph: f(x)=|x| .Graph: f(x)=|x| .Use the graph of the function to find its domain and range. Write the domain and range in interval notation.Use the graph of the function to find its domain and range. Write the domain and range in interval notation.Use the graph of the function to find the indicated values. (a) Find: f(0) . (b) Find: f(12) . (c) Find: f(32) . (d) Find the values for xwhen f(x)=0 . (e) Find the x-intercepts. (f) Find the y-intercepts. (g) Find the domain. Write it in interval notation. (h) Find the range. Write it in interval notation.Use the graph of the function to find the indicated values. (a) Find: f(0) . (b) Find: f() . (c) Find: f() . (d) Find the values for xwhen f(x)=0 . (e) Find the x-intercepts. (f) Find the y-intercepts. (g) Find the domain. Write it in interval notation. (h) Find the range. Write it in interval notation.In the following exercises, determine whether each graph is the graph of a function. 337. (a) (b)In the following exercises, determine whether each graph is the graph of a function. 338. (a) (b)In the following exercises, determine whether each graph is the graph of a function. 339. (a) (b)In the following exercises, determine whether each graph is the graph of a function. 340. (a) (b)In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 341. f(x)=3x+4In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 342. f(x)=2x+5In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 343. f(x)=x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 344. f(x)=4x3In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 345. f(x)=2x+2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 346. f(x)=3x+3In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 347. f(x)=12x+1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 348. f(x)=23x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 349. f(x)=5In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 350. f(x)=2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 351. f(x)=3In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 352. f(x)=1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 353. f(x)=2xIn the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 354. f(x)=3xIn the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 355. f(x)=2xIn the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 356. f(x)=3xIn the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 357. f(x)=3x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 358. f(x)=2x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 359. f(x)=3x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 360. f(x)=2x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 361. f(x)=12x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 362. f(x)=13x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 363. f(x)=x21In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 364. f(x)=x2+1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 365. f(x)=2x3In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 366. f(x)=2x3In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 367. f(x)=x3+2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 368. f(x)=x32In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 369. f(x)=2xIn the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 370. f(x)=2xIn the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 371. f(x)=x1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 372. f(x)=x+1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 373. f(x)=3|x|In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 374. f(x)=2|x|In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 375. f(x)=|x|+1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 376. f(x)=|x|1In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation. 377.In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation. 378.In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation. 379.In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation. 380.In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation. 381.In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation. 382.In the following exercises, use the graph of the function to find the indicated values. 383. (a) Find: f(0) . (b) Find: f(12) . (c) Find: f(32) . (d) Find the values for xwhen f(x)=0 . (e) Find the x-intercepts. (f) Find the y-intercepts. (g) Find the domain. Write it in interval notation. (h) Find the range. Write it in interval notation.In the following exercises, use the graph of the function to find the indicated values. 384. (a) Find: f(0) . (b) Find: f() . (c) Find: f() . (d) Find the values for xwhen f(x)=0 . (e) Find the x-intercepts. (f) Find the y-intercepts. (g) Find the domain. Write it in interval notation. (h) Find the range. Write it in interval notationIn the following exercises, use the graph of the function to find the indicated values. 385. (a) Find: f(0) . (b) Find: f(3) . (c) Find: f(3) . (d) Find the values for xwhen f(x)=0 . (e) Find the x-intercepts. (f) Find the y-intercepts. (g) Find the domain. Write it in interval notation. (h) Find the range. Write it in interval notation.In the following exercises, use the graph of the function to find the indicated values. 386. (a) Find: f(0) . (b) Find the values for xwhen f(x)=0 . (c) Find the x-intercepts. (d) Find the y-intercepts. (e) Find the domain. Write it in interval notation. (f) Find the range. Write it in interval notationExplain in your own words how to find the domain from a graph.Explain in your own words how to find the range from a graph.Explain in your own words how to use the vertical line test.Draw a sketch of the square and cube functions. What are the similarities and differences in the graphs?In the following exercises, plot each point in a rectangular coordinate system. 391. (a) (1,5) (b) (3,4) (c) (2,3) (d)(1,52)In the following exercises, plot each point in a rectangular coordinate system. 392. (a) (2,0) (b) (0,4) (c) (0,5) (d) (3,0)In the following exercises, plot each point in a rectangular coordinate system. 393. 5x+y=10 (a) (5,1) (b) (2,0) (c) (4,10)In the following exercises, plot each point in a rectangular coordinate system. 394. y=6x2 (a) (1,4) (b) (13,0) (c) (6,2)In the following exercises, graph by plotting points. 395. y=4x3In the following exercises, graph by plotting points. 396. y=3xIn the following exercises, graph by plotting points. 397. y=12x+3In the following exercises, graph by plotting points. 398. y=45x1In the following exercises, graph by plotting points. 399. xy=6In the following exercises, graph by plotting points. 400. 2x+y=7In the following exercises, graph by plotting points. 401. 3x2y=6In the following exercises, graph each equation. 402. y=2In the following exercises, graph each equation. 403. x=3In the following exercises, graph each pair of equations in the same rectangular coordinate system. 404. y=2x and y=2In the following exercises, graph each pair of equations in the same rectangular coordinate system. 405. y=43x and y=43In the following exercises, find the x- and y-intercepts. 406.In the following exercises, find the x- and y-intercepts. 407.In the following exercises, find the intercepts of each equation. 408. xy=1In the following exercises, find the intercepts of each equation. 409. x+2y=6In the following exercises, find the intercepts of each equation. 410. 2x+3y=12In the following exercises, find the intercepts of each equation. 411. y=34x12In the following exercises, find the intercepts of each equation. 412. y=3xIn the following exercises, find the intercepts of each equation. 413. x+3y=3In the following exercises, find the intercepts of each equation. 414. xy=4In the following exercises, find the intercepts of each equation. 415. 2xy=5In the following exercises, find the intercepts of each equation. 416. 2x4y=8In the following exercises, find the intercepts of each equation. 417. y=4xIn the following exercises, find the slope of each line shown. 418.In the following exercises, find the slope of each line shown. 419.In the following exercises, find the slope of each line shown. 420.In the following exercises, find the slope of each line shown. 421.In the following exercises, find the slope of each line. 422. y=2In the following exercises, find the slope of each line. 423. x=5In the following exercises, find the slope of each line. 424. x=3In the following exercises, find the slope of each line. 425. y=1In the following exercises, use the slope formula to find the slope of the line between each pair of points. 426. (1,1),(0,5)In the following exercises, use the slope formula to find the slope of the line between each pair of points. 427. (3.5),(4,1)In the following exercises, use the slope formula to find the slope of the line between each pair of points. 428. (5,2),(3,2)In the following exercises, use the slope formula to find the slope of the line between each pair of points. 429. (2,1),(4,6)In the following exercises, graph each line with the given point and slope. 430. (2,2);m=52In the following exercises, graph each line with the given point and slope. 431. (3,4);m=13In the following exercises, graph each line with the given point and slope. 432.x-intercept 4;m=3In the following exercises, graph each line with the given point and slope. 433.y-intercept 1; m=34In the following exercises, identify the slope and y-intercept of each line. 434. y=4x+9In the following exercises, identify the slope and y-intercept of each line. 435. y=53x6In the following exercises, identify the slope and y-intercept of each line. 436. 5x+y=10In the following exercises, identify the slope and y-intercept of each line. 437. 4x5y=8In the following exercises, graph the line of each equation using its slope and y-intercept. 438. y=2x+3In the following exercises, graph the line of each equation using its slope and y-intercept. 439. y=x1In the following exercises, graph the line of each equation using its slope and y-intercept. 440. y=25x+3In the following exercises, graph the line of each equation using its slope and y-intercept. 441. 4x3y=12In the following exercises, determine the most convenient method to graph each line. 442. x=5In the following exercises, determine the most convenient method to graph each line. 443. y=3In the following exercises, determine the most convenient method to graph each line. 444. 2x+y=5In the following exercises, determine the most convenient method to graph each line. 445. xy=2In the following exercises, determine the most convenient method to graph each line. 446. y=22x+2In the following exercises, determine the most convenient method to graph each line. 447. y=34x1Katherine is a private chef. The equation C=6.5m+42 models the relation between her weekly cost, C, in dollars and the number of meals, m, that she serves. (a) Find Katherine’s cost for a week when she serves no meals. (b) Find the cost for a week when she serves 14 meals. (c) Interpret the slope and C-intercept of the equation. (d) Graph the equation.Marjorie teaches piano. The equation P=35h250 models the relation between her weekly profit, P, in dollars and the number of studentlessons, s, that she teaches. (a) Find Marjorie’s profit for a week when she teachesno student lessons. (b) Find the profit for a week when she teaches 20 student lessons. (c) Interpret the slope and P-intercept of the equation. (d) Graph the equation.In the following exercises, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither. 450. 4x3y=1;y=43x3In the following exercises, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither. 451. y=5x1;10x+2y=0In the following exercises, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither. 452. 3x2y=5;2x+3y=6In the following exercises, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither. 453. 2xy=8;x2y=4In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slopeintercept form. 454. slope 13 and y-intercept (0,6)In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slopeintercept form. 455. slope 5 and y-intercept (0,3)In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slopeintercept form. 456. slope 0 and y-intercept (0,4)In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slopeintercept form. 457. slope 2 and y-intercept (0,0)In the following exercises, find the equation of the line shown in each graph. Write the equation in slopeintercept form. 458.In the following exercises, find the equation of the line shown in each graph. Write the equation in slopeintercept form. 459.In the following exercises, find the equation of the line shown in each graph. Write the equation in slopeintercept form. 460.In the following exercises, find the equation of the line shown in each graph. Write the equation in slopeintercept form. 461.In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slopeintercept form. 462. m=14 , point (8,3)In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slopeintercept form. 463. m=35 , point (10,6)In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slopeintercept form. 464. Horizontal line containing (2,7)In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slopeintercept form. 465. m=2 , point (1,3)In the following exercises, find the equation of a line containing the given points. Write the equation in slopeintercept form. 466. (2,10) and (2,2)In the following exercises, find the equation of a line containing the given points. Write the equation in slopeintercept form. 467. (7,1) and (5,0)In the following exercises, find the equation of a line containing the given points. Write the equation in slopeintercept form. 468. (3,8) and (3,4)In the following exercises, find the equation of a line containing the given points. Write the equation in slopeintercept form. 469. (5,2) and (1,2)In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slopeintercept form. 470. line y=3x+6 , point (1,5)In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slopeintercept form. 471. line 2x+5y=10 , point (10,4)In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slopeintercept form. 472. line x=4 , point (2,1)In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slopeintercept form. 473. line y=5 , point (4,3)In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slopeintercept form. 474. line y=45x+2 , point (8,9)In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slopeintercept form. 475. line 2x3y=9 , point (4,0)In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slopeintercept form. 476. line y=3 , point (1,3)In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slopeintercept form. 477. line x=5 point (2,1)In the following exercises, determine whether each ordered pair is a solution to the given inequality. 478. Determine whether each ordered pair is a solution to the inequality yx3 : (a) (0,1) (b) (2,4) (c) (5,2) (d) (3,1) (e) (1,5)In the following exercises, determine whether each ordered pair is a solution to the given inequality. 479. Determine whether each ordered pair is a solution to the inequality x+y4 : (a) (6,1) (b) (3,6) (c) (3,2) (d) (5,10) (e) (0,0)In the following exercises, write the inequality shown by the shaded region. 480. Write the inequality shown by the graph with the boundary line y=x+2 .In the following exercises, write the inequality shown by the shaded region. 481. Write the inequality shown by the graph with the boundary line y=23x3 .In the following exercises, write the inequality shown by the shaded region. 482. Write the inequality shown by the shaded region in the graph with the boundary line x+y=4 .In the following exercises, write the inequality shown by the shaded region. 483. Write the inequality shown by the shaded region in the graph with the boundary line x2y=6 .In the following exercises, graph each linear inequality. 484. Graph the linear inequality y25x4 .In the following exercises, graph each linear inequality. 485. Graph the linear inequality y14x+3 .In the following exercises, graph each linear inequality. 486. Graph the linear inequality xy5 .In the following exercises, graph each linear inequality. 487. Graph the linear inequality 3x+2y10 .In the following exercises, graph each linear inequality. 488. Graph the linear inequality y3x .In the following exercises, graph each linear inequality. 489. Graph the linear inequality y6 .Shanthie needs to earn at least $500 a week during her summer break to pay for college. She works two jobs. One as a swimming instructor that pays $10an hour and the other as an intern in a law office for$25 hour. How many hours does Shanthie need to work at each job to earn at least $500 per week? (a) Let x be the number of hours she works teaching swimming and let y be the number of hours she worksas an intern. Write an inequality that would model thissituation. (b) Graph the inequality. (c) Find three ordered pairs (x,y) that would be solutions to the inequality. Then, explain what that means for Shanthie.Atsushi he needs to exercise enough to burn 600 calories each day. He prefers to either run or bike and burns 20 calories per minute while running and 15 calories a minute while biking. (a) If x is the number of minutes that Atsushi runs and yis the number minutes he bikes, find the inequality that models the situation. (b) Graph the inequality. (c) List three solutions to the inequality. What options do the solutions provide Atsushi?In the following exercises, for each relation, (a) find the domain of the relation (b) find the range of the relation. 492. {(5,2),(5,4),(7,6)(8,8),(9,10)}In the following exercises, for each relation, (a) find the domain of the relation (b) find the range of the relation. 493. {(3,7),(2,3),(1,9)(0,3),(1,8)}In the following exercise, use the mapping of the relation to (a) list the ordered pairs of the relation (b) find the domain of the relation (c) find the range of the relation. 494. The mapping below shows the average weight of a child according to age.In the following exercise, use the graph of the relation to (a) list the ordered pairs of the relation (b) find the domain of the relation (c) find the range of the relation. 495.In the following exercises, use the set of ordered pairs to (a) determine whether the relation is a function (b) find the domain of the relation (c) find the range of the relation. 496. {(9,5),(4,3),(1,1)(0,0),(1,1),(4,3),(9,5)}In the following exercises, use the set of ordered pairs to (a) determine whether the relation is a function (b) find the domain of the relation (c) find the range of the relation. 497. {(3,27),(2,8),(1,1)(0,0),(1,1),(2,8),(3,27)}In the following exercises, use the mapping to (a) determine whether the relation is a function (b) find the domain of the function (c) find the range of the function. 498.In the following exercises, use the mapping to (a) determine whether the relation is a function (b) find the domain of the function (c) find the range of the function. 499.In the following exercises, determine whether each equation is a function. 500. 2x+y=3In the following exercises, determine whether each equation is a function. 501. y=x2In the following exercises, determine whether each equation is a function. 502. y=3x5In the following exercises, determine whether each equation is a function. 503. y=x3In the following exercises, determine whether each equation is a function. 504. 2x+y2=4In the following exercises, evaluate the function: (a) f(2)(b) f(3)(c) f(a). 505. f(x)=3x4In the following exercises, evaluate the function: (a) f(2)(b) f(3)(c) f(a). 506. f(x)=2x+5In the following exercises, evaluate the function: (a) f(2)(b) f(3)(c) f(a). 507. f(x)=x25x+6In the following exercises, evaluate the function: (a) f(2)(b) f(3)(c) f(a). 508. f(x)=3x22x+1In the following exercises, evaluate the function. 509. g(x)=3x25x;g(2)In the following exercises, evaluate the function. 510. F(x)=2x23x+1;F(1)In the following exercises, evaluate the function. 511. h(x)=4|t1|+2;h(3)In the following exercises, evaluate the function. 512. f(x)=x+2x1;f(3)In the following exercises, determine whether each graph is the graph of a function. 513.In the following exercises, determine whether each graph is the graph of a function. 514.In the following exercises, determine whether each graph is the graph of a function. 515.In the following exercises, determine whether each graph is the graph of a function. 516.In the following exercises, determine whether each graph is the graph of a function. 517.In the following exercises, determine whether each graph is the graph of a function. 518.In the following exercises, determine whether each graph is the graph of a function. 519.In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 520. f(x)=5x+1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 521. f(x)=4x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 522. f(x)=23x1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 523. f(x)=6In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 524. f(x)=2xIn the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 525. f(x)=3x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 526. f(x)=12x2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 527. f(x)=x2+2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 528. f(x)=x32In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 529. f(x)=x+2In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 530. f(x)=|x|In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 531. f(x)=|x|+1In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation 532.In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation 533.In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation 534.In the following exercises, use the graph of the function to find the indicated values. 535. (a) Find f(0) . (b) Find f(12) . (c) Find f(32) . (d) Find the values for xwhen f(x)=0 . (e) Find the x-intercepts. (f) Find the y-intercepts. (g) Find the domain. Write it in interval notation. (h) Find the range. Write it in interval notation.In the following exercises, use the graph of the function to find the indicated values. 536. (a) Find f(0) . (b) Find the values for xwhen f(x)=0 . (c) Find the x-intercepts. (d) Find the y-intercepts. (e) Find the domain. Write it in interval notation. (f) Find the range. Write it in interval notation.Plot each point in a rectangular coordinate system. (a) (2,5) (b) (1,3) (c) (0,2) (d) (4,32) (e) (5,0)Which of the given ordered pairs are solutions to the equation 3xy=6 ? (a) (3,3) (b) (2,0) (c) (4,6)Find the slope of each line shown. 539. (a) (b)Find the slope of each line shown. 540. Find the slope of the line between the points (5,2) and (1,4) .Find the slope of each line shown. 541. Graph the line with slope 12 containing the point (3,4) .Find the slope of each line shown. 542. Find the intercepts of 4x+2y=8 and graph.Graph the line for each of the following equations. 543. y=53x1Graph the line for each of the following equations. 544. y=xGraph the line for each of the following equations. 545. y=2Find the equation of each line. Write the equation in slope-intercept form. 546. slope 34 and y-intercept (0,2) .Find the equation of each line. Write the equation in slope-intercept form. 547. m=2 , point (3,1)Find the equation of each line. Write the equation in slope-intercept form. 548. containing (10,1) and (6,1)Find the equation of each line. Write the equation in slope-intercept form. 549. perpendicular to the line y=54x+2 , containing the point (10,3)Find the equation of each line. Write the equation in slope-intercept form. 550. Write the inequality shown by the graph with the boundary line y=x3 .Graph each linear inequality. 551. y32x+5Graph each linear inequality. 552. xy4Graph each linear inequality. 553. y5xGraph each linear inequality. 554. Hiro works two part time jobs in order to earn enough money to meet her obligations of at least $450 a week. Her job at the mall pays $10 an hour and her administrative assistant job on campus pays $15 an hour. How many hours does Hiro need to work at each job to earn at least $450? (a) Let x be the number of hours she works at the mall and let y be the number of hours she works as administrative assistant. Write an inequality that would model this situation. (b) Graph the inequality . (c) Find three ordered pairs (x,y) that would be solutions to the inequality. Then explain what that means for Hiro.Graph each linear inequality. 555. Use the set of ordered pairs to (a) determine whether the relation is a function, (b) find the domain of the relation, and (c) find the range of the relation. {(3,27),(2,8),(1,1),(0,0),(1,1),(2,8),(3,27)}Graph each linear inequality. 556. Evaluate the function: (a) f(1) (b) f(2) (c) f(c) . f(x)=4x22x3Graph each linear inequality. 557. For h(y)=3|y1|3 , evaluate h(4) .Graph each linear inequality. 558. Determine whether the graph is the graph of a function. Explain your answer.In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 559. f(x)=x2+1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 560. f(x)=x+1In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. 561. (a) Find the y-intercepts. (b) Find f(1) . (c) Find f(1) . (d) Find the domain. Write it in interval notation.Determine whether the ordered pair is a solution to the system {3x+y=0x+2y=5 . (a) (1,3) (b) (0,0)Determine whether the ordered pair is a solution to the system {x3y=83xy=4 . (a) (2,2) (b) (2,2)Solve the system by graphing: {x3y=3x+y=5 .Solve the system by graphing: {x+y=13x+2y=12 .Solve the system by graphing: {x+y=12x+y=10 .Solve the system by graphing: {2x+y=6x+y=1 .Solve the system by graphing: {y=14x+2x+4y=8 .