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Sagot :
To solve the problem, we need to identify which set of coordinate pairs matches the function rule: multiply the [tex]\( x \)[/tex] value by 2, then subtract 1. The function can be expressed as:
[tex]\[ y = 2x - 1 \][/tex]
We are given four different sets of coordinate pairs, and we need to determine which set satisfies this function rule. Let's evaluate each set:
### Set 1: [tex]\((5, 9), (9, 17), (14, 27), (25, 49)\)[/tex]
1. For [tex]\( (5, 9) \)[/tex]:
[tex]\[ y = 2(5) - 1 = 10 - 1 = 9 \][/tex]
2. For [tex]\( (9, 17) \)[/tex]:
[tex]\[ y = 2(9) - 1 = 18 - 1 = 17 \][/tex]
3. For [tex]\( (14, 27) \)[/tex]:
[tex]\[ y = 2(14) - 1 = 28 - 1 = 27 \][/tex]
4. For [tex]\( (25, 49) \)[/tex]:
[tex]\[ y = 2(25) - 1 = 50 - 1 = 49 \][/tex]
All pairs in Set 1 satisfy the function rule.
### Set 2: [tex]\((5, 9), (14, 25), (9, 17), (27, 49)\)[/tex]
1. For [tex]\( (5, 9) \)[/tex]:
[tex]\[ y = 2(5) - 1 = 10 - 1 = 9 \][/tex]
2. For [tex]\( (14, 25) \)[/tex]:
[tex]\[ y = 2(14) - 1 = 28 - 1 = 27 \][/tex]
3. For [tex]\( (9, 17) \)[/tex]:
[tex]\[ y = 2(9) - 1 = 18 - 1 = 17 \][/tex]
4. For [tex]\( (27, 49) \)[/tex]:
[tex]\[ y = 2(27) - 1 = 54 - 1 = 53 \][/tex]
The pair [tex]\( (14, 25) \)[/tex] and [tex]\( (27, 49) \)[/tex] do not satisfy the function rule.
### Set 3: [tex]\((5, 9), (9, 17), (17, 14), (14, 25)\)[/tex]
1. For [tex]\( (5, 9) \)[/tex]:
[tex]\[ y = 2(5) - 1 = 10 - 1 = 9 \][/tex]
2. For [tex]\( (9, 17) \)[/tex]:
[tex]\[ y = 2(9) - 1 = 18 - 1 = 17 \][/tex]
3. For [tex]\( (17, 14) \)[/tex]:
[tex]\[ y = 2(17) - 1 = 34 - 1 = 33 \][/tex]
4. For [tex]\( (14, 25) \)[/tex]:
[tex]\[ y = 2(14) - 1 = 28 - 1 = 27 \][/tex]
The pairs [tex]\( (17, 14) \)[/tex] and [tex]\( (14, 25) \)[/tex] do not satisfy the function rule.
### Set 4: [tex]\((5, 11), (9, 17), (14, 29), (25, 51)\)[/tex]
1. For [tex]\( (5, 11) \)[/tex]:
[tex]\[ y = 2(5) - 1 = 10 - 1 = 9 \][/tex]
2. For [tex]\( (9, 17) \)[/tex]:
[tex]\[ y = 2(9) - 1 = 18 - 1 = 17 \][/tex]
3. For [tex]\( (14, 29) \)[/tex]:
[tex]\[ y = 2(14) - 1 = 28 - 1 = 27 \][/tex]
4. For [tex]\( (25, 51) \)[/tex]:
[tex]\[ y = 2(25) - 1 = 50 - 1 = 49 \][/tex]
The pairs [tex]\( (5, 11) \)[/tex], [tex]\( (14, 29) \)[/tex], and [tex]\( (25, 51) \)[/tex] do not satisfy the function rule.
### Conclusion
Set 1 is the only set where all coordinate pairs match the given function rule [tex]\( y = 2x - 1 \)[/tex].
The set of coordinate pairs that matches the function rule is:
[tex]\[(5, 9), (9, 17), (14, 27), (25, 49)\][/tex]
Thus, the answer is Set 1.
[tex]\[ y = 2x - 1 \][/tex]
We are given four different sets of coordinate pairs, and we need to determine which set satisfies this function rule. Let's evaluate each set:
### Set 1: [tex]\((5, 9), (9, 17), (14, 27), (25, 49)\)[/tex]
1. For [tex]\( (5, 9) \)[/tex]:
[tex]\[ y = 2(5) - 1 = 10 - 1 = 9 \][/tex]
2. For [tex]\( (9, 17) \)[/tex]:
[tex]\[ y = 2(9) - 1 = 18 - 1 = 17 \][/tex]
3. For [tex]\( (14, 27) \)[/tex]:
[tex]\[ y = 2(14) - 1 = 28 - 1 = 27 \][/tex]
4. For [tex]\( (25, 49) \)[/tex]:
[tex]\[ y = 2(25) - 1 = 50 - 1 = 49 \][/tex]
All pairs in Set 1 satisfy the function rule.
### Set 2: [tex]\((5, 9), (14, 25), (9, 17), (27, 49)\)[/tex]
1. For [tex]\( (5, 9) \)[/tex]:
[tex]\[ y = 2(5) - 1 = 10 - 1 = 9 \][/tex]
2. For [tex]\( (14, 25) \)[/tex]:
[tex]\[ y = 2(14) - 1 = 28 - 1 = 27 \][/tex]
3. For [tex]\( (9, 17) \)[/tex]:
[tex]\[ y = 2(9) - 1 = 18 - 1 = 17 \][/tex]
4. For [tex]\( (27, 49) \)[/tex]:
[tex]\[ y = 2(27) - 1 = 54 - 1 = 53 \][/tex]
The pair [tex]\( (14, 25) \)[/tex] and [tex]\( (27, 49) \)[/tex] do not satisfy the function rule.
### Set 3: [tex]\((5, 9), (9, 17), (17, 14), (14, 25)\)[/tex]
1. For [tex]\( (5, 9) \)[/tex]:
[tex]\[ y = 2(5) - 1 = 10 - 1 = 9 \][/tex]
2. For [tex]\( (9, 17) \)[/tex]:
[tex]\[ y = 2(9) - 1 = 18 - 1 = 17 \][/tex]
3. For [tex]\( (17, 14) \)[/tex]:
[tex]\[ y = 2(17) - 1 = 34 - 1 = 33 \][/tex]
4. For [tex]\( (14, 25) \)[/tex]:
[tex]\[ y = 2(14) - 1 = 28 - 1 = 27 \][/tex]
The pairs [tex]\( (17, 14) \)[/tex] and [tex]\( (14, 25) \)[/tex] do not satisfy the function rule.
### Set 4: [tex]\((5, 11), (9, 17), (14, 29), (25, 51)\)[/tex]
1. For [tex]\( (5, 11) \)[/tex]:
[tex]\[ y = 2(5) - 1 = 10 - 1 = 9 \][/tex]
2. For [tex]\( (9, 17) \)[/tex]:
[tex]\[ y = 2(9) - 1 = 18 - 1 = 17 \][/tex]
3. For [tex]\( (14, 29) \)[/tex]:
[tex]\[ y = 2(14) - 1 = 28 - 1 = 27 \][/tex]
4. For [tex]\( (25, 51) \)[/tex]:
[tex]\[ y = 2(25) - 1 = 50 - 1 = 49 \][/tex]
The pairs [tex]\( (5, 11) \)[/tex], [tex]\( (14, 29) \)[/tex], and [tex]\( (25, 51) \)[/tex] do not satisfy the function rule.
### Conclusion
Set 1 is the only set where all coordinate pairs match the given function rule [tex]\( y = 2x - 1 \)[/tex].
The set of coordinate pairs that matches the function rule is:
[tex]\[(5, 9), (9, 17), (14, 27), (25, 49)\][/tex]
Thus, the answer is Set 1.
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