Question

Upward shape graph with vertex (3,0) and points (2,1),(4,1),(1,2),(5,2),(0,3),(6,3),(-1,4),(7,4),(-2,5)
What is the domain of the relation above
All real numbers greater than or equal to 0
All real numbers
All real numbers between-6, and -4
All real numbers greater than -2

Answer 1

All real numbers between-6 and 4

Answer 2

To determine the domain of the relation represented by the given points, we need to identify the x-coordinates of all the points listed. The points provided are:

- (2, 1)
- (4, 1)
- (1, 2)
- (5, 2)
- (0, 3)
- (6, 3)
- (-1, 4)
- (7, 4)
- (-2, 5)

The x-coordinates are:
- 2
- 4
- 1
- 5
- 0
- 6
- -1
- 7
- -2

Now, let's list all these x-coordinates together:
-2, -1, 0, 1, 2, 4, 5, 6, 7

The smallest x-coordinate is -2 and the largest is 7. Therefore, the domain of the relation is all x-values represented by the points, which can be expressed in interval notation as:

**Domain:** \([-2, 7]\)

None of the options you've provided seem to match this domain exactly. However, if we interpret the options:

1. **All real numbers greater than or equal to 0** - Incorrect, as there are negative values in the domain (-2).
2. **All real numbers** - Incorrect, as the x-values are limited to -2 through 7.
3. **All real numbers between -6 and -4** - Incorrect, as this range does not include most x-values we have.
4. **All real numbers greater than -2** - This is partially acceptable, but it excludes -2 itself, which is part of the domain.

Thus, none of the provided options accurately describe the domain of the relation considering all the x-coordinates of the points listed. If you are looking for the best match, option 4 is the closest one, but it's still not entirely correct.

Answer 3

Thank you for the clarification regarding the options. Let's re-evaluate the domain based on your updated option:

We look at the given points:
- (2, 1)
- (4, 1)
- (1, 2)
- (5, 2)
- (0, 3)
- (6, 3)
- (-1, 4)
- (7, 4)
- (-2, 5)

Focusing on the x-coordinates:
- The x-coordinates are: -2, -1, 0, 1, 2, 4, 5, 6, 7.

From this, we can determine the range of x-values:
- The smallest x-coordinate is -2, and the largest x-coordinate is 7.

So, all the x-coordinates take values from -2 to 7.

Now, regarding the option provided, "All real numbers between -6 and 4":

- This option implies a range of (-6, 4), which does not accurately cover the domain we established based on the x-coordinates. The number -2 is included, and other points go up to 7.

### Conclusion:
The correct domain of the relation, based on the x-coordinates derived from the points, is \([-2, 7]\). The option "All real numbers between -6 and 4" does not represent the domain accurately since it only includes values less than 4 and doesn't extend to -2 or the maximum of 7.

If you have further clarifications or specifics on the options, please let me know!