M-370 4 Answers.cwk (WP)

Math 370
Chapter 4 Answers
4–1 Answers
1. 3, –3, –1, 1/ 2
2. –5, –1, 3, –1/ 4
3. –3, 1, 2 , –1/ 2
4. 0 , 3 , –2, –1/ 2 , –1/ 2
5. 0, 1, –1, 2 , 3
6. 1. –1 , 2 , –2 , 3
7. –1 . 2. –2, 3/ 2 , 3/ 2
8. –1. –2 , 3, 1/ 2 , 3/ 2
9. 2, ± 5
10. –1, –2, ± 3
11. 1, –1, 3/ 2, ± 2
12. 3, –2, ± 7
13. 3, –1, −2 ± 6
14. –5, 1, ±
16. –2, 1/ 3, ± 3i
17.
19.
2, –2, –1, ± 2i
3
3
15. –3, 1/ 2, ± 2i
1, –1, 6, 1 ± 3i
20.
18. 4, –3, 1/ 2, ± 3i
2, –2, −1 ± i 3
Section 4– 2
1. x ∈ ℜ: x ∈ (−∞,−4 ] or [−1, 2]
–1
–4
x ∈ ℜ: x ∈ [−2,−1] or x = 0
2
3. x ∈ℜ: x ∈ (−∞,−2 ) or (3,∞)
–2
2.
4.
3
0
6.
x ∈ℜ: x ∈ (−∞,−2 ) or (0,3)
0
0
8.
1
9 . x ∈ℜ: x ∈ [3.∞ )
3
x ∈ ℜ: x ∈ (−∞,0]
1
7. x ∈ ℜ: x = −5 or x = 1
–5
0
–2
5. x ∈ ℜ: x = −5 or x ∈ [0,1]
–5
–1
–2
x ∈ ℜ: x ∈ (−∞ ,0) or (0,1) or ( 4,∞ )
0
1
4
10. No real Numbers
3
11.
x ∈ℜ: x ∈ (−∞,−3] or [16,∞ ) or 0
–3
0
12. x ∈ ℜ: x ∈ (−∞,−3] or [0,6]
16
Math 370 Chap. 4 – 14 Answers
–3
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6
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13. x ∈ ℜ: x ∈ (0 ,∞ )
14. x ∈ ℜ: x ∈ (−∞,4 ] or [7,∞)
0
15.
7
16. x ∈ℜ: x ∈ [−5,−1) or (1,∞)
x ∈ ℜ: x ∈ (−∞,−3) or [2,∞)
–3
17.
4
–5
2
x ∈ ℜ: x ∈ (−∞,0) or (3,5)
0
3
1
18. x ∈ ℜ: x ∈ (−∞,−4 ) or (2,∞)
5
19. x ∈ ℜ: x ∈ (5,∞)
2
–4
20 x ∈ ℜ: x ∈ (−∞,−4 ] or (−2,1] or (2,∞ )
–4 –2
5
21. x ∈ ℜ: x ∈ (−∞,0] or [1,3) or (3,∞)
1
0
–1
1
2
22. x ∈ ℜ: x ∈ [−2,∞ )
3
–2
4–3 Answers
2a. +∞
2b. +∞
3a. −∞
3b. −∞
4a. −∞
4b. +∞
5a. −∞
5b. −∞
6a. +∞
6b. −∞
7a. −∞
7b. +∞
8a. +∞
8b. +∞
9a. +∞
9b. +∞
10a. +∞
10b. −∞
11a. +∞
11b. +∞
12a. −∞
12b. +∞
13a. +∞
13b. +∞
14a. +∞
14b. −∞
15a. −∞
15b. +∞
16a. −∞
16b. −∞
17a. −∞
17b. +∞
18a. −∞
18b. −∞
19a. −∞
19b. +∞
20a. +∞
20b. −∞
21a. −∞
21b. +∞
22a. +∞
22b. +∞
23a. −∞
23b. +∞
24a. −∞
24. −∞
1a.
1b.
+∞
−∞
4 – 4A Answers
1a. 0
1b. 0
2a. 3/ 2
2b. 3/ 2
3a. +∞
3b. +∞
4a. 0
4b. 0
5a. +∞
5b. −∞
6a. −∞
6b. −∞
7a. –1/ 3
7b. –1/ 3
8a. 0
8b. 0
9a. − ∞
9b. +∞
10a. –2/ 3
10b. –2/ 3
11a. 0
11b. 0
12a. −∞
12b. +∞
13a. +∞
13b. +∞
14a. 3
14b. 3
15a. 0
15b. 0
16a. +∞
16b. −∞
17a. − ∞
17b. +∞
18a. –2
18b. –2
Math 370 Chap. 4 – 14 Answers
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19a. 0
19b. 0
20a. –1/ 2
20b. –1/ 2
21a. – 9/ 2
21b. – 9/ 2
22a. 1/ 2
22b. 1/ 2
24a. +∞
24b. −∞
23a. 4/ 3
23b. 4/ 3
4 – 4B Answers
1a. +∞
1b. −∞
2a. +∞
2b.
1c. DNE
1d. +∞
1e. +∞
+∞
2c. +∞
2d. 3
2e. 3
3a. −∞
3b. −∞
3c. −∞
3d. 2
3e. 2
4a. +∞
4b. −∞
4c. DNE
4d. 0
4e. 0
5a. −∞
5b. −∞
5c. −∞
5d. −∞
5e. +∞
6a. −∞
6b.
6c. DNE
6d. −∞
6e. −∞
7a. −∞
7b. −∞
7c. −∞
7d. –2
7e. –2
8a. +∞
8b.
+∞
8c. +∞
8d. +∞
8e. −∞
9a. −∞
9b. +∞
9c. DNE
9d. +∞
9e. −∞
9f. DNE
9g. 0
10a. −∞
10b. −∞
10c. −∞
10d. +∞
10e. −∞
10f. DNE
10g. +∞ 10h. −∞
11a. +∞
11b. −∞
11c. DNE
11d. −∞
11e. +∞
11f. DNE
11g. –4 11h. –4
12a. +∞
12b. +∞
12c. +∞
12d. +∞
12e. +∞
12f. +∞
12g. 3
13a. −∞
13b. +∞
13c. DNE
13d. −∞
13e. −∞
13f. DNE
13g. −∞ 13h. −∞
14a. +∞
14b. +∞
14c. +∞
14d. −∞
14e. +∞
14f. DNE
14g. +∞ 14h. +∞
15a. −∞
15b. +∞
15c. DNE
15d. +∞
15e. −∞
15f. DNE
15g. 0
16a. −∞
16b. −∞
16c. −∞
16d. +∞
16e. +∞
16f. +∞
16g. +∞ 16h. +∞
1. VA at x = 1 Hole at ( –3, 1/ 2 )
1a. +∞
1b. −∞
1c. DNE
1d. 1/ 2
1e. 1/ 2
1f. 1/ 2
2. VA at x = –3 Hole at ( –1, –3/ 8 )
2a. –3/ 8
2b. –3/ 8
2c . –3/ 8
2d. +∞
2e. +∞
2f. +∞
3. VA at x = 1 Hole at ( –1, –3/ 20 )
3a. +∞
3b. +∞
3c . +∞
3d. –3/ 20
3e. –3/ 20
3f. –3/ 20
4. VA at x = –2 Hole at ( 1, 0 )
4a. +∞
4b. −∞
4c . DNE
4d. 0
4e. 0
4f. 0
+∞
9h. 0
12h. 3
15h. 0
Rational Functions 4 – 4C Answers
Math 370 Chap. 4 – 14 Answers
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5. VA at x = 5 Hole at ( 0, 12/ 25 )
5a. +∞
5b. +∞
5c . +∞
5e. 12/ 25
5f. 12/ 25
6. VA at x = –2 Holes at ( 0, 0 ) and ( –3 , –9 )
6a. 0
6b. –9
6c . +∞
6d. −∞
6e. –3
6f. –3
7. VA at x = –1 Holes at ( 0, 2/ 3 ) and ( –1 , 0 )
7a. 2/ 3
7b. 0
7c . +∞
7d. +∞
7e. –2
7f. –2
8. VA at x = 3 Holes at ( 0, 8/ 3 )and (2 , 0 )
8a. 8/ 3
8b. 0
8c . +∞
8d. −∞
8e. 0
8f. 0
9. VA at x = 0 Hole at ( –3, –2/ 9 )
9a. −∞
9b. −∞
9c. −∞
5d. 12/ 25
9d. –2/ 9 9e. –2/ 9
9f. –2/ 9
9g. 0
9h. 0
10h. 0
10. VA at x = 1 and x = –3 Hole at (0 , 2/ 9 )
10a. −∞
10b. +∞
10c. DNE
10d. +∞
10e. +∞
10f. +∞
10g. 0
11. VA at x = 4 Hole at ( 3, –2 )
11a. –2
11b. –2
11c. –2
11d. +∞
11e. −∞
11f. DNE
11g. 0 11h. 0
12. VA at x = 1 Hole at ( –3, 0 )
12a. +∞
12b. −∞
12c. DNE
12d. 0
12e. 0
12f. 0
12g. +∞
12h. −∞
13. VA at x = –2 Hole at ( –1, –8 )
13a. –8
13b. –8
13c. –8
13d. −∞
13e. −∞
13f. −∞
13g. −∞
13h. −∞
14. VA at x = –2 Hole at ( 0, 0 )
14a. 0
14b. 0
14c. 0
14d. +∞
14e. −∞
14f. DNE
14g. 2
14h.2
15. VA at x = 3 Hole at ( –3, 7/ 6 )
15a. 7/ 6
15b. 7/ 6
15c. 7/ 6
15d. −∞
15e. +∞
15f. DNE
15g. –1
15h.–1
16. VA at x = 2 Hole at ( 0, 0 )
16a. 0
16b. 0
16c. 0
16d. +∞
16e. −∞
15f. DNE
15g. 1
15h. 1
17. VA at x = 0 Hole at ( 3, 0)
17a. −∞
17b. +∞
17c.. DNE
17d. 0
17e. 0
17f. 0
17g. –1/ 2 17h.–1/ 2
18. VA at x = –5 Hole at ( 0, 0)
18a. –2/ 5 18b. –2/ 5
18c. –2/ 5
18d. +∞
18e. −∞
18f. DNE
18g. 1
18h.1
14 – 5
1a. 4
1b. –2
1c. DNE
2a. 4
2b. 4
2c. 4
3a. 6
3b. 6
3c. 6
4a. –3
4b. 2
4c. DNE
5a. 3
5b. 3
5c. 3
6a. 1
6b. 3
6c. DNE
7a. 1
7b. 2
7c. DNE
8a. 4
8b. 4
8c. 4
10b. 7
10c. DNE
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9a. 1
9b. 1
9c. 1
Math 370 Chap. 4 – 14 Answers
10a. 6
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11a. 0
11b. 0
11c. 0
12a. 9
12b. 7
12c. DNE
13a. 5
13b. 5
13c. 5
13d. –1
13e. –1
13f. –1
14a. 4
14b. 2
14c. DNE
14d. –2
14e. –2
14f. –2
15a. 0
15b. 4
15c. DNE
15d. –4
15e. 0
15f. DNE
16a. 3
16b. 3
16c. 3
16d. 3
16e. 2
16f. DNE
17a. 0
17b. 3
17c. DNE
18a. 2
18b. 2
18c. 2
19a. 7
19b. 3
19c. DNE
20a. 5
20b. 5
20c. 5
21a. 4
21b. 0
21c. DNE
22a. 3
22b. –1
22c. DNE
23a. 2
23b. 2
23c. 2
24a. –6
24b. –6
24c. –6
25a. DNE
25b. –5
26a. DNE
26b. 5
Math 370 Chap. 4 – 14 Answers
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