Math Problem Statement

Choose the correct interval notation for the graph. (You get only one try for the answer; be careful.)

Interval Notation

(-∞, -3] ⋃ [3,7)

(-∞, -3) ⋃ (3,7)

[-∞, -3) ⋃ [-3,7]

(-∞, -3) ⋃ [3, 7] None of these

Solution

To determine the correct interval notation for the graph, we need to interpret the notation provided:

  1. (,3][3,7)(-∞, -3] ⋃ [3,7)
  2. (,3)(3,7)(-∞, -3) ⋃ (3,7)
  3. [,3)[3,7][-∞, -3) ⋃ [-3,7]
  4. (,3)[3,7](-∞, -3) ⋃ [3, 7]
  5. None of these

Here’s a quick review of interval notation:

  • (,a)(-∞, a): All numbers less than aa, not including aa.
  • (,a](-∞, a]: All numbers less than or equal to aa, including aa.
  • (a,b)(a, b): All numbers between aa and bb, not including aa or bb.
  • [a,b)[a, b): All numbers between aa and bb, including aa but not bb.
  • [a,b][a, b]: All numbers between aa and bb, including both aa and bb.

Considering each option:

  1. (,3][3,7)(-∞, -3] ⋃ [3,7) includes all numbers less than or equal to 3-3 and all numbers from 33 to 77, including 33 but not 77.
  2. (,3)(3,7)(-∞, -3) ⋃ (3,7) includes all numbers less than 3-3 and all numbers from 33 to 77, not including 33 or 77.
  3. [,3)[3,7][-∞, -3) ⋃ [-3,7] is incorrect because [,3)[-∞, -3) is not a proper interval notation.
  4. (,3)[3,7](-∞, -3) ⋃ [3, 7] includes all numbers less than 3-3 and all numbers from 33 to 77, including 33 and 77.

If we visualize these on a number line, it becomes clearer which intervals include the boundary points:

  • If 3-3 is included (closed interval at 3-3), then we must have ,3]-∞, -3].
  • If 33 is included (closed interval at 33), then we must have [3,[3,.

So, the correct choice based on typical interval conventions would be the one that includes these specific boundaries correctly.

Considering the provided intervals:

  • (,3][3,7)(-∞, -3] ⋃ [3,7) includes 3-3 and excludes 77, which might match common graphing conventions.

Therefore, the correct interval notation for the graph is:

(-∞, -3] ⋃ [3,7).

Do you want details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How do you determine whether to use a square bracket or a parenthesis in interval notation?
  2. Can you explain the difference between an open interval and a closed interval?
  3. How would you represent the interval where all numbers between -5 and 5 are included, but not -5 and 5 themselves?
  4. What is the union of the intervals [1,4][1, 4] and (3,5](3, 5]?
  5. How can interval notation be used to describe the domain of a function?

Tip: Always sketch a number line when working with interval notation to visually confirm which points are included or excluded.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Interval Notation
Set Theory

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12