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

3 answers

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.

All real numbers between-6 and 4

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!