Question

Select all of the following tables which represent y
as a function of x and are one-to-one.
x -3 10 15
y 4 7 13
x 3 10 15
y 4 7 7
x 3 10 10
y 4 7 13

Answer 1

To determine which of the provided tables represent \( y \) as a function of \( x \) and whether they are one-to-one, we need to check both the definition of a function (each \( x \) should map to exactly one \( y \)) and the definition of a one-to-one function (each \( y \) value should correspond to exactly one \( x \) value).

Let's analyze each table:

1. **Table 1**:
```
x: -3 10 15
y: 4 7 13
```
- Each \( x \) corresponds to one \( y \):
- \(-3 \to 4\)
- \(10 \to 7\)
- \(15 \to 13\)
- No \( y \) value repeats.
- Conclusion: This table can be considered a function and is one-to-one.

2. **Table 2**:
```
x: 3 10 15
y: 4 7 7
```
- Each \( x \) corresponds to one \( y \):
- \(3 \to 4\)
- \(10 \to 7\)
- \(15 \to 7\)
- The \( y \) value of \( 7 \) is repeated for two different \( x \) values (10 and 15).
- Conclusion: This table is a function but not one-to-one.

3. **Table 3**:
```
x: 3 10 10
y: 4 7 13
```
- \( x \) value \( 10 \) corresponds to two different \( y \) values:
- \(3 \to 4\)
- \(10 \to 7\) and \(10 \to 13\)
- Since \( 10 \) has more than one mapping in \( y \), this does not satisfy the definition of a function.
- Conclusion: This table is not a function.

### Summary:

The only table that represents \( y \) as a function of \( x \) and is one-to-one is:

- **Table 1**:
```
x: -3 10 15
y: 4 7 13
```