Question
Which relation is a function of x? pick one answer {(1, 2), (7, 6), (3, 2), (1, 0), (5, 6)}
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 0, 0, 0. Column 2 is labeled y with entries 2, negative 6, 9, negative 7.
x = 3 y squared minus 7
On a coordinate plane, a graph curves up, then curves down, and then curves up again.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 0, 0, 0. Column 2 is labeled y with entries 2, negative 6, 9, negative 7.
x = 3 y squared minus 7
On a coordinate plane, a graph curves up, then curves down, and then curves up again.
Answers
GPT-4o mini
To determine which relation is a function of \( x \), we need to identify if each relation passes the vertical line test, meaning that each value of \( x \) must correspond to exactly one value of \( y \).
1. **Set of ordered pairs: \{(1, 2), (7, 6), (3, 2), (1, 0), (5, 6)\}**
- The pairs (1, 2) and (1, 0) both share the same \( x \) value of 1 but have different \( y \) values. This means that the relation is not a function.
2. **2-column table with 4 rows:**
- The \( x \) column has all entries as 0 (0, 0, 0, 0). This means multiple \( y \) values (2, -6, 9, -7) correspond to the same \( x \) value (0). Hence, this relation is also not a function.
3. **Equation: \( x = 3y^2 - 7 \)**
- Rearranging gives us \( y^2 = \frac{x + 7}{3} \). This shows that for a given positive \( x \) value, there can be two corresponding \( y \) values (one positive and one negative) unless \( x + 7 = 0\) (where \( y = 0 \)). Therefore, this relation is not a function.
4. **Graphical representation:**
- The graph described as curving up, then down, and then curving up again likely contains more than one \( y \) value for at least one \( x \) value, indicating it is not a function.
Based on the evaluations above, none of the relations presented are functions of \( x \). If you have a specific option to choose from that wasn't included in your message, please share it, and I can help assess it as well.
1. **Set of ordered pairs: \{(1, 2), (7, 6), (3, 2), (1, 0), (5, 6)\}**
- The pairs (1, 2) and (1, 0) both share the same \( x \) value of 1 but have different \( y \) values. This means that the relation is not a function.
2. **2-column table with 4 rows:**
- The \( x \) column has all entries as 0 (0, 0, 0, 0). This means multiple \( y \) values (2, -6, 9, -7) correspond to the same \( x \) value (0). Hence, this relation is also not a function.
3. **Equation: \( x = 3y^2 - 7 \)**
- Rearranging gives us \( y^2 = \frac{x + 7}{3} \). This shows that for a given positive \( x \) value, there can be two corresponding \( y \) values (one positive and one negative) unless \( x + 7 = 0\) (where \( y = 0 \)). Therefore, this relation is not a function.
4. **Graphical representation:**
- The graph described as curving up, then down, and then curving up again likely contains more than one \( y \) value for at least one \( x \) value, indicating it is not a function.
Based on the evaluations above, none of the relations presented are functions of \( x \). If you have a specific option to choose from that wasn't included in your message, please share it, and I can help assess it as well.