Question
Which relation is a function of x?
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 2, 3. Column 2 is labeled y with entries 7, negative 9, 8, negative 4.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 8, negative 8, 1, 1. Column 2 is labeled y with entries negative 9, 2, negative 9, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 5, negative 5, negative 5. Column 2 is labeled y with entries 1, 7, negative 9, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 2, 4, 7. Column 2 is labeled y with entries negative 1, 5, 0, negative 1.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 2, 3. Column 2 is labeled y with entries 7, negative 9, 8, negative 4.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 8, negative 8, 1, 1. Column 2 is labeled y with entries negative 9, 2, negative 9, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 5, negative 5, negative 5. Column 2 is labeled y with entries 1, 7, negative 9, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 2, 4, 7. Column 2 is labeled y with entries negative 1, 5, 0, negative 1.
Answers
GPT-4o mini
To determine which relation is a function of \( x \), we need to check if each \( x \) value in the table corresponds to exactly one \( y \) value. If any \( x \) value is paired with multiple \( y \) values, then that relation is not a function.
1. **First Table:**
- \( x = -1 \) → \( y = 7 \)
- \( x = 2 \) → \( y = -9 \)
- \( x = 2 \) → \( y = 8 \) (This is a repeated x with a different y)
- \( x = 3 \) → \( y = -4 \)
- **Not a function** (since \( x = 2 \) maps to two different \( y \) values)
2. **Second Table:**
- \( x = -8 \) → \( y = -9 \)
- \( x = -8 \) → \( y = 2 \) (This is a repeated x with a different y)
- \( x = 1 \) → \( y = -9 \)
- \( x = 1 \) → \( y = 2 \) (This is a repeated x with a different y)
- **Not a function** (since \( x = -8 \) and \( x = 1 \) each map to two different \( y \) values)
3. **Third Table:**
- \( x = -5 \) → \( y = 1 \)
- \( x = -5 \) → \( y = 7 \) (This is a repeated x with a different y)
- \( x = -5 \) → \( y = -9 \) (This is another same x with a different y)
- \( x = -5 \) → \( y = 2 \) (This is yet another same x with a different y)
- **Not a function** (since \( x = -5 \) maps to multiple \( y \) values)
4. **Fourth Table:**
- \( x = -3 \) → \( y = -1 \)
- \( x = -2 \) → \( y = 5 \)
- \( x = 4 \) → \( y = 0 \)
- \( x = 7 \) → \( y = -1 \)
- **Is a function** (as each \( x \) value is unique and maps to exactly one \( y \) value)
Based on the analysis, the fourth table is the only relation that is a function of \( x \).
1. **First Table:**
- \( x = -1 \) → \( y = 7 \)
- \( x = 2 \) → \( y = -9 \)
- \( x = 2 \) → \( y = 8 \) (This is a repeated x with a different y)
- \( x = 3 \) → \( y = -4 \)
- **Not a function** (since \( x = 2 \) maps to two different \( y \) values)
2. **Second Table:**
- \( x = -8 \) → \( y = -9 \)
- \( x = -8 \) → \( y = 2 \) (This is a repeated x with a different y)
- \( x = 1 \) → \( y = -9 \)
- \( x = 1 \) → \( y = 2 \) (This is a repeated x with a different y)
- **Not a function** (since \( x = -8 \) and \( x = 1 \) each map to two different \( y \) values)
3. **Third Table:**
- \( x = -5 \) → \( y = 1 \)
- \( x = -5 \) → \( y = 7 \) (This is a repeated x with a different y)
- \( x = -5 \) → \( y = -9 \) (This is another same x with a different y)
- \( x = -5 \) → \( y = 2 \) (This is yet another same x with a different y)
- **Not a function** (since \( x = -5 \) maps to multiple \( y \) values)
4. **Fourth Table:**
- \( x = -3 \) → \( y = -1 \)
- \( x = -2 \) → \( y = 5 \)
- \( x = 4 \) → \( y = 0 \)
- \( x = 7 \) → \( y = -1 \)
- **Is a function** (as each \( x \) value is unique and maps to exactly one \( y \) value)
Based on the analysis, the fourth table is the only relation that is a function of \( x \).