More Related Content More from Nittaya Noinan (17) 3. A B A
B
1 {1, 2} {3, 4, 5} {(1, 3), (1, 4), (1, 5), (2, 3),
(2, 4), (2, 5)}
2 {a} {1, 2} {(a, 1), (a, 2)}
3 {3, 4} {a, b, c}
4 {2, 4} {5, 6}
5 {a, b} {3, 4, 5,
6}
6 {1, 2, 3} {5, 7, 9}
7 {a, b, c} {2, 4}
8 {x, y} {1, 2, 3}
9 {1, 2} {1, 2}
10 {m, n} {x, y}
4. 1.
2. (10, 6)
3. (2, 3) ( 4 , 3)
4.
4.1
4.1 (x, y) = (6, 9)
……………………
4.2 (x – 2, 4) = (8, y + 2)
…….
4.3 (-3, a) = (b – 4, 6)
4.2
4.4 (x + y, x – y) = (6, 4)
……………………
4.5 (2x, y) = (16, 2)
…….
4.3
……………………
…….
4.4
5. ……………………
…….
4.5
……………………
…….
1. A = {3} B = {5, 6}
1.1 A B =
………………………………………………………………….
1.2 B A =
………………………………………………………………….
1.3 A A =
………………………………………………………………….
1.4 B B =
………………………………………………………………….
2. A = {1, 3} B = {5, 7, 9}
2.1 A B =
………………………………………………………………….
2.2 B A =
………………………………………………………………….
6. 2.3 A A =
………………………………………………………………….
2.4 B B =
………………………………………………………………….
3. A = {2, 4} B = {6, 8, 10, 12}
3.1 A B
=……………………………………………
3.2 B B
=……………………………………………
2
1. r = {(2, 4), (3, 7), (1, 5)}
7. 2. r = {(0, 0), (-1, -1), (-2, -2), (-3, -3), (-4, -
4)}
3. r = {(x, y) I I | x2 + y2 = 4}
x
y
8. 4. r = {(x, y) I I | y = x + 3}
x
y
4. r = {(x, y) | 2 x 5}
9. 5. r = {(x, y) | y = x2 - 2 }
x
y
3
1. r = {(1, 2), (2, 4), (3, 5), (4, 6)}
1.1 Dr =
………………………………………………………………
…
1.2 Rr =
11. 1 {(1, a), (2, b), (3, c), (4,
d)}
2 {(2, 10), (3, 20), (4, 30),
(5, 40)}
3 {(1, 3), (2, 4), (3, 5), (4,
6)}
4 {(0, 0), (1, 1), (2, 2), (3,
3)}
5 {(1, 4), (2, 5), (3, 6), (4,
7)}
6 {(1, 1), (2, 4), (3, 9), (4,
16)}
7 {(0, 0), (1, 2), (2, 4), (3,
6), (4, 8)}
8 {(x, y) | y = x - 4}
9 {(x, y) I I | y = x2 +
1}
10 {(x, y) | y = x-8}
12. 4
1 r = {(1, 2), (3, 7), (4, 9), (8,
6), (10, 8)}
2 r = {(3, 2), (4, 2), (6, 2)}
3 r = {(1, 3), (2, 4), (3, 6), (3,
8)}
4 r = {(x, y) | y = x2 - 1}
5 r = {(x, y) | xy = 2}
6 r = {(x, y) | y2 = x + 3}
13. 7 r = {(x, y) | y = x3}
8 r = {(x, y) | y = x2 + 3}
9 r = {(2, 3), (2, 4), (3, 6), (4,
9)}
10 r = {(x, y) | x = y2 + 2y + 1}
1 r1 = {(3, 2), (-1, 4), (0, 2), (5, -
3)}
2 r2 = {(1, -1), (-1, -1), (0, 1), (3,
1)}
3 r3 = {(4, 2), (4, 3), (5, 4), (6,
6)}
4 r4 = {(6, 1), (6, 1), (7, 2), (8,
3), (9, 4)}
5 r5 = {(2, 1), (2, 3), (3, 4), (4,
5), (5, 6)}
6 r6 = {(x, y) | y = 3x – 1}
7 r7 = {(x, y) | y = 3x2– x + 3}
8 r8 = {(x, y) | y = 2x2 + 1}
9 r9 = {(x, y) | y = 4x2}
14. 10 r10 = {(x, y) | x2 + y2 = 4 , x
0}
f = {(1, 2), (2, 4), . Y
(3, 6), (4, 8)}
1-3
0 X
1. f
. y = 2x
Y . Y
. y = 3x
. y = 2x + 1 1
. y 0= x + 1 X x 2 4 6 08
2. Y fX f(x 1 2 3 4
x 0 2 3 4
)
3. f(x 2 4 6 8 f
x 2 4 6 4
. )
X f(x 1 2 3 8
0 .
x 1 2 3 4
)
f(x 2 4 6 8
. )
.
.
.
15. 1 f = {(2, 5), (3, 7), (4, 9), {2, 3, 4, {5, 7, 9,
(5, 11)} 5} 11}
2 f = {(a, 1), (b, 2), (c, 3),
(d, 4)}
3 f = {(m, 2), (n, 4), (p, 6)}
4 f = {(4, 7), (6, 9), (8, 11)}
5 f = {(2, 1), (3, 2), (4, 3),
(5, 4)}
6 f = {(a, 10), (b, 10), (c,
10)}
7 f = {(3, 6), (5, 10), (7, 14)}
8 f = {(1, 4), (2, 5), (3, 6),
(4, 7)}
1. y = x2 – 1
x
y
16. 2. y = 4x
x
y
3. y = 3x 1
2x - 2
x
y
18. 6. y2 = x , x ≥ 0
x
y
7. y = 3x - 1
x
y
20. 1. f(x) = 2x2 – x + 5
1.1 f(4)
1.2 f(-2)
1.3 f(a + 3)
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2. f(x) = 3x – 5
2.1 f(-3)
2.2 f(6)
24. x
y
x
y
2. y1 =
-x
y2 = -x + 1
y3 = -x - 2
x
y
26. y2 = x + 3
y3 = x - 4
x
y
x
y
x
y
27. X Y
1. y = 2x + 8
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2. y = - x + 10
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3. y = x + 7
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32. 1.1 y = 5x2
1.2 y = -3x2
1.3 y = 12x2
1.4 y = -6x2
1.5 y = x2 +
1
1.6 y = x2 -
2
1.7 y = (x -
1)2
1.8 y = -(x +
1)2
1.9 y = (x -
2)2 + 1
1.1 y = (x +
0 1)2 -3
1.1 y = (x -
1 3)2- 1
1.1 y = -(x +
2 1)2 + 2
1.1 y = -(x +
3 8)2 – 6
1.1 y = 2(x –
4 4 )2 + 3
33. 1.1 y = -4(x +
5 4)2 – 10
2.
2.1 y = x2 2.2 y = x2 + 1 2.3 y = x2 - 1
x
y
x
y
x
y
34. 3.
3.1 y = -x2 3.2 y = -x2 + 2 3.3 y = -x2 - 1
x
y
x
y
35. x
y
4.
4.1 y = (x – 1)2 4.2 y = (x – 1)2+ 2 4.3 y =
(x – 1)2- 3
x
37. 5.
5.1 y = - (x – 2)2 5.2 y = - (x – 2)2+ 2 5.3 y = -
(x – 2)2- 3
x
y
x
y
x
y
38. 6.
6.1 y = x2 6.2 y = x2 + 2 6.3 y = x2 +4x
+ 4
x
y
x
y
x
y
39. 1. y = x2 – 2x – 3
…………………………………………………………………………
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.
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.
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.
43. …………………………………………………………………………
.
4. y = 3x2 + 12x + 3
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.
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.
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47. x2 – 1 x2 + 2x – 3
……….
y = x2 – 1 a(x – h)2 + k
Y x2 + 2x – 3 =
Y …….. ………………………
X =
x2 –1 = 0 ………………………
( )( ) = 0 a = ….. , h =
x = ……….. x …….. k = ……
= ………… a>0 y
= x2 + 2x – 3
……………
0
X
x2 + 2x – 3 = 0
x y 0 ( )( ) = 0
y 0 x = ……….. x
………………………... = …………..
x2 1 X
………………………... ………………
0
48. x2 + 2x – 3 0
……………………
9
1. x
45
1.1 x
1.2
45
x
1.3 45
164
1.4 x
52. …………………………………………………………………………
.
4.
f(t) = -t2 + 7t t
4.1
4.2
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.
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54. 1. y = 3x
x
y
2. y = 22x
x
y
55. x
3. y = 1
3
x
y
11
1. 2x = 64
2x
4. 1
128
64
56. x
2. 1 1
5. (0.01)
1
4 64 1,000,000
x
3. 1
81 6. (81)x = 729
27
1 x
1.1 16x = 4 1.1
57. x
1.2 1
16 ……………………
2
1.3 (4) x 1 ………..
64
1.4 3x
1 1.2
243
1.5 5 2x 625
……………………
………..
1.3
……………………
………..
1.4
……………………
………..
1.5
……………………
………..
2
850,000
f(n) =
850,000(1.08)n n
5
60. 3. f(x) = | x + 2 | + 4
x
y
4. f(x) = | x - 2 | + 2
x
y
61. 1 |x+5| = 0
2 |x-6| = 0
3 |x| - 2 = 0
4 |x+2| - 4 = 0
5 |x+5| = 5
6 |x+3| - 1 = 0
7 |x-4| = 6
8 |x+1| - 5 = 0
9 |x+4| - 3 = 0
10 |x| = 7
62. 13
2 , 0 x 20
3 , 20 x 100
1. f(x)
5 , 100 x 250
9 , 250 x 500
16 , 500 x 1,000
30 , 1,000 x 2,000
66. …………………………………………………………………………
.
3. f(x)
15 , 0 x 1,000
10 , x 1,000
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