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Unformatted text preview: A Selected Answers 1.1.1. (2 / 3) x + (1 / 3) 1.1.2. y = − 2 x 1.1.3. ( − 2 / 3) x + (1 / 3) 1.1.4. y = 2 x + 2, 2, − 1 1.1.5. y = − x + 6, 6, 6 1.1.6. y = x/ 2 + 1 / 2, 1 / 2, − 1 1.1.7. y = 3 / 2, y-intercept: 3 / 2, no x-intercept 1.1.8. y = ( − 2 / 3) x − 2, − 2, − 3 1.1.9. yes 1.1.10. y = 0, y = − 2 x + 2, y = 2 x + 2 1.1.11. y = 75 t , 164 minutes 1.1.12. y = (9 / 5) x + 32, ( − 40 , − 40) 1.1.13. y = 0 . 15 x + 10 1.1.14. . 03 x + 1 . 2 1.1.15. (a) y = braceleftBigg ≤ x < 100 ( x/ 10) − 10 100 ≤ x ≤ 1000 x − 910 1000 < x 1.1.16. y = braceleftBigg . 15 x ≤ x ≤ 19450 . 28 x − 2528 . 50 19450 < x ≤ 47050 . 33 x − 4881 47050 < x ≤ 97620 1.1.17. (a) P = − . 0001 x + 2 (b) x = − 10000 P + 20000 1.1.18. (2 / 25) x − (16 / 5) 1.2.1. (a) x 2 + y 2 = 9 (b) ( x − 5) 2 + ( y − 6) 2 = 9 (c) ( x + 5) 2 + ( y + 6) 2 = 9 1.2.2. (a) Δ x = 2, Δ y = 3, m = 3 / 2, y = (3 / 2) x − 3, √ 13 (b) Δ x = − 1, Δ y = 3, m = − 3, y = − 3 x + 2, √ 10 (c) Δ x = − 2, Δ y = − 2, m = 1, y = x , √ 8 1.2.6. ( x + 2 / 7) 2 + ( y − 41 / 7) 2 = 1300 / 49 1.3.1. { x | x ≥ 3 / 2 } 1.3.2. { x | x negationslash = − 1 } 1.3.3. { x | x negationslash = 1 and x negationslash = − 1 } 1.3.4. { x | x < } 1.3.5. { x | x ∈ R } , i.e., all x 451 452 Appendix A Selected Answers 1.3.6. { x | x ≥ } 1.3.7. { x | h − r ≤ x ≤ h + r } 1.3.8. { x | x ≥ 1 } 1.3.9. { x | − 1 / 3 < x < 1 / 3 } 1.3.10. { x | x ≥ 0 and x negationslash = 1 } 1.3.11. { x | x ≥ 0 and x negationslash = 1 } 1.3.12. R 1.3.13. { x | x ≥ 3 } , { x | x ≥ } 1.3.14. A = x (500 − 2 x ), { x | ≤ x ≤ 250 } 1.3.15. V = r (50 − πr 2 ), { r | < r ≤ radicalbig 50 /π } 1.3.16. A = 2 πr 2 +2000 /r , { r | < r < ∞} 2.1.1. − 5, − 2 . 47106145, − 2 . 4067927, − 2 . 400676, − 2 . 4 2.1.2. − 4 / 3, − 24 / 7, 7 / 24, 3 / 4 2.1.3. − . 107526881, − . 11074197, − . 1110741, − 1 3(3 + Δ x ) → − 1 9 2.1.4. 3 + 3Δ x + Δ x 2 1 + Δ x → 3 2.1.5. 3 . 31, 3 . 003001, 3 . 0000, 3 + 3Δ x + Δ x 2 → 3 2.1.6. m 2.2.1. 10, 25 / 2, 20, 15, 25, 35. 2.2.2. 5, 4 . 1, 4 . 01, 4 . 001, 4 + Δ t → 4 2.2.3. − 10 . 29, − 9 . 849, − 9 . 8049, − 9 . 8 − 4 . 9Δ t → − 9 . 8 2.3.1. 7 2.3.2. 5 2.3.3. 2.3.4. undefined 2.3.5. 1 / 6 2.3.6. 2.3.7. 3 2.3.8. 172 2.3.9. 2.3.10. 2 2.3.11. does not exist 2.3.12. √ 2 2.3.13. 3 a 2 2.3.14. 512 2.3.15. − 4 2.3.16. 2.3.18. (a) 8, (b) 6, (c) dne, (d) − 2, (e) − 1, (f) 8, (g) 7, (h) 6, (i) 3, (j) − 3 / 2, (k) 6, (l) 2 2.4.1. − x/ radicalbig 169 − x 2 2.4.2. − 9 . 8 t 2.4.3. 2 x + 1 /x 2 2.4.4. 2 ax + b 2.4.5. 3 x 2 2.4.8. − 2 / (2 x + 1) 3 / 2 2.4.9. 5 / ( t + 2) 2 2.4.10. y = − 13 x + 17 2.4.11. − 8 3.1.1. 100 x 99 3.1.2. − 100 x − 101 3.1.3. − 5 x − 6 3.1.4. πx π − 1 3.1.5. (3 / 4) x − 1 / 4 3.1.6. − (9 / 7) x − 16 / 7 3.2.1. 15 x 2 + 24 x 3.2.2. − 20 x 4 + 6 x + 10 /x 3 3.2.3. − 30 x + 25 3.2.4. 6 x 2 + 2 x − 8 Appendix A Selected Answers...
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