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7 , b = 2, (4, 5); (c) m = 2, b = 4, (1, 2); (d) m = 0, b = 2, (1, 2); 4
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4.10 (a) m = 5, b = 4, (1, 9); (b) m = 4 (e) m = , b = 4, (3, 0). 3 4.11 k = 9. 4.12 No.
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1 4.13 (a) Yes; (c) in all cases; (d) k = . 4 4.14 (a) Parallel; (b) neither; (c) parallel; (d) perpendicular; (e) neither. 4.15 (a) y = 9 x + 32; (b) 40 . 5
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4.17 (a) y =
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4.18 (12, 9) is not on the line; (6, 3) is on the line. 4.22 4x + 3y 9 > 0 and x > 1; see Fig. A-5. 4.23 x < 200/3. 4.24 See Fig. A-6.
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4.26 (a) All nonvertical lines through the point (0, 2); (b) all lines with slope 3. 4.27 (a) Horizontal lines; (b) (i) 2; (ii) 14; (iii) 1 ; (iv) 3; (v) none 5
2 1 43 4.28 (a) y = x + 3; (b) y = x + 9; (c) y = x + . 3 6 12
5.4 (a) (2, 0); (b) (0, 2); (c) (7, 1) and (2, 6); (d) (1, 2) and (3, 18); (e) (0, 0) and (1, 1); 3 3 1 1 ( f ) (2, 2) and (2, 2); (g) , and , ; (h) (4, 1) and ( 1, 4); 2 2 2 2 (i) 9 6 13, 13 13 13 and 9 6 13, 13 ; ( j) null set. See Fig. A-7. 13 13
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6.6 (a) y-axis; (b) origin; (c) x-axis, y-axis, origin; (d) x-axis, y-axis, origin; (e) x-axis; ( f ) none; (g) origin; (h) none; (i) y-axis; ( j) y-axis; (k) origin; (l) none. 6.7 (a) x 2 + xy + y2 = 1; (b) y3 + xy2 x 3 = 8; (c) x 2 + 12x 3y = 1; (d) y = 3x + 1; (e) no change.
7.8 (Let R denote the set of real numbers. In each answer, the rst set is the domain, the second set the range. The graphs are sketched in Fig. A-8.) (a) R, ( , 4]; (b) [0, ), ( , 0]; (c) [ 2, 2], range of H is [0, 2], range of J is [ 2, 0]; (d) ( , 2] [2, ) (union or sum of the two intervals), [0, ); (e) R, [0, ); ( f ) R, set of all integers; (g) R, set of all integers; (h) R {0} (set of all real numbers except 0), R {0}; (i) R {1}, R {0}; ( j) R, R; (k) R, R; (l) R, [2, ); (m) {1, 2, 4}, { 1, 3}; (n) R { 2}, R { 4}; (o) R, ( , 2] {4}; (p) R {0}, { 1, 1}; (q) R, [2, ); (r) R, R; (s) R, [0, 1); (t) R, R. 7.10 (c) and (d). 2 x 1 7.11 (a) f (x) = 3 , domain is R {0}; (b) f (x) = , domain is R { 1}; (c) f (x) = x, domain is R. x+1 x 7.12 (a) Domain is R {2, 3}, range is (0, ) ( , 4]; (b) ( 1, 1), [1, ); (c) ( 1, ), (0, 2]; (d) [0, 4), [ 1, 2]; (e) R, [0, ). 7.13 (a) k = 8; (b) f is not de ned when x = 0, but g is. 7.14 Of the in nitely many correct answers, some examples are: (a) f (x) = 2x for 0 < x < 1; (b) f (x) = 5x 1 for 0 x < 1; 0 if x = 0 ; (d) f (x) = (x 1)2 + 1 for x < 1 or 1 < x < 2. (c) f (x) = 1 if x > 0 7.15 (a) y-axis; (b) none; (c) y-axis for both; (d) y-axis; (e) none; ( f ) none; (g) none; (h) origin; (i) none; ( j) origin; (k) origin; (l) none; (m) none; (n) none; (o) none; (p) origin; (q) none; (r) none; (s) none; (t) origin. 7.16 (a) Even; (b) neither; (c) both even; (d) even; (e) neither; ( f ) neither; (g) neither; (h) odd; (i) neither; ( j) odd; (k) odd; (l) neither; (m) neither; (n) neither; (o) neither; (p) odd; (q) neither; (r) neither; (s) neither; (t) odd. 7.17 (a) No: (b) yes; (c) k = 0; (d) k = 2; (e) yes; f (x) = 0 for all x. 1 1 |x + h| |x| 7.18 (a) 2x + h 2; (b) 1; (c) 3x 2 + 3hx + h2 ; (d) . ; (e) 5; ( f ) h x+h+ x x+h+ x 7.19 (a) 1, 1, 3, 3; (b) 2, 4, 4; (c) 2, 2, 3; (d) 2; (e) 2, 3, 4; ( f ) 2, 1 + 7.20 One, two (one of them repeated), or three. 7.21 (a) k = 3; (b) k = 2. 2, 1 2; (g) 4, 2, 2. 7.22 9 and 12. 7.23 (iii).
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