Question

Which represents a function
x 3 4 5 6
y-1 0 3 4
x y
-4 -7
-1 -2
0 3
Arrows from -4 to -7
-1 to 3
0 to -2
5 to -7
Graph sideways u shape points (-10),(1,-1.5),(4,-4)
{(-4,3),(-2,3),(0,2),(5,2)}
x y
0 2
4 3
9 4
5
Arrow from 9 to 4 and 5
Graph downward u shape points (1,1), (-1,0), (3,0), (-2,5),(4,-5)

Answer 1

To determine whether a relation represents a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). Here’s an analysis of each section provided:

1. **First group (x=3, 4, 5, 6; y=-1, 0, 3, 4)**:
- The relation appears to be:
- (3, -1)
- (4, 0)
- (5, 3)
- (6, 4)
- Each x-value has a unique y-value. This represents a function.

2. **Second group (arrows)**:
- The pairs include:
- (-4, -7)
- (-1, 3)
- (0, -2)
- (5, -7)
- Again, each x-value points to a unique y-value. This is also a function.

3. **Third group (points)**:
- The points are:
- (-10, y)
- (1, -1.5)
- (4, -4)
- Since we have not been given y-values for all x-values and we're unsure of the mappings, we can't definitively say this is a function without the y-value for x = -10.

4. **Fourth group {(-4,3),(-2,3),(0,2),(5,2)}**:
- Here, we see:
- (-4, 3)
- (-2, 3)
- (0, 2)
- (5, 2)
- The x-values -4 and -2 both map to the same y-value (3) but they still represent unique inputs. Therefore, despite multiple outputs for some inputs, this is NOT a function.

5. **Fifth group (x, y values)**:
- The pairs:
- (0, 2)
- (4, 3)
- (9, 4)
- Each x-value corresponds to a unique y-value. This represents a function.

6. **Sixth group (other arrows)**:
- The values include:
- Arrow from 9 to 4 and 5
- This suggests that the same input x = 9 maps to multiple outputs (y = 4 and y = 5). Hence, this does NOT represent a function.

7. **Seventh group (graph points)**:
- The points are:
- (1, 1)
- (-1, 0)
- (3, 0)
- (-2, 5)
- (4, -5)
- Each x-value has a unique y-value, so this represents a function.

### Summary:
- **Functions**: First group, second group, third group (if y-value is defined), fifth group, and seventh group.
- **Not functions**: Fourth group and sixth group.

If you need to assess or analyze additional information or need clarification on any point, let me know!

Answer 2

Third group is (-1,0) instead of (-10,y)

Answer 3

Thank you for the clarification! Let's analyze the third group again with the correct coordinates provided:

### Third group:
- Points:
- (-1, 0)
- (1, -1.5)
- (4, -4)

Now let's re-evaluate whether this represents a function.

Each x-value here:
- \(x = -1\) maps to \(y = 0\)
- \(x = 1\) maps to \(y = -1.5\)
- \(x = 4\) maps to \(y = -4\)

Since each x-value is unique and corresponds to exactly one y-value, this set of points also represents a function.

### Updated Summary:
- **Functions**: First group, second group, third group, fifth group, and seventh group.
- **Not functions**: Fourth group and sixth group.

If there's anything else you'd like to discuss or any other groups to analyze, just let me know!