Question

Which relation represents a function choose all that apply
A. x 3 4 5 6
y -1 0 3 4
B. x y
-4 -7
-1 3
0 -2
5 -7
C. Curved v shape graph points
(-1,0), (0,-1), (2,-2), (3,3), (5,5),(5,-5)
D. {(-4,3), (-2,3)(0,2),(5,2)}
E. x y
0 2
4 3
9 4, 5
F. Graph downward u shape points (1,4),(0,3), (-1,0),(3,0),(-2,-5), (4,-5)

Answer 1

To determine whether a relation represents a function, we must check that for each input \( x \), there is exactly one output \( y \). This means that no two ordered pairs can have the same \( x \)-value with different \( y \)-values.

Let's analyze each option:

**A.**
```
x: 3 4 5 6
y: -1 0 3 4
```
- Each \( x \)-value (3, 4, 5, 6) maps to exactly one \( y \)-value. This is a function.

**B.**
```
x: -4 -1 0 5
y: -7 3 -2 -7
```
- Each \( x \)-value (-4, -1, 0, 5) maps to exactly one \( y \)-value (although -7 is repeated for \( x = -4 \) and \( x = 5 \), it does not violate the function definition). This is a function.

**C.** (points (-1,0), (0,-1), (2,-2), (3,3), (5,5),(5,-5))
- The point (5, -5) shares the same \( x \)-value (5) as (5, 5) but has a different \( y \)-value. This is not a function.

**D.**
```
{(-4,3), (-2,3), (0,2),(5,2)}
```
- Each \( x \)-value (-4, -2, 0, 5) maps to exactly one \( y \)-value (although -2 and 0 map to the same \( y \)-value (2), this still conforms to the function definition). This is a function.

**E.**
```
x: 0 4 9
y: 2 3 4, 5
```
- The \( x \)-value 9 maps to two \( y \)-values (4 and 5). This is not a function.

**F.** (downward U shape)
Points: (1,4), (0,3), (-1,0), (3,0), (-2,-5), (4,-5)
- The points (3, 0) and (-2, -5) do not share any \( x \)-values with different \( y \)-values, indicating that no input has multiple outputs. However, we don't necessarily know if this relation might have overlapping \( x \)-values in the curve itself without seeing the graph. But based on the points provided, it can be classified as a function (no repeated \( x \)-values).

### Conclusion:
The relations that represent functions are:
- **A**
- **B**
- **D**
- **F** (based on the provided points)

So, the relations that represent functions are: **A, B, D, and F**.