Which of the following choices corresponds to the graph? 

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


(
−
∞
,
4
]
(
-
∞
,
4
]


[
4
,
∞
)
[
4
,
∞
)


(
−
∞
,
4
)
(
-
∞
,
4
)


It looks like you're asking to identify which interval or inequality corresponds to a specific graph. However, to determine the correct choice, we need to establish what kind of graph is being referred to. Typically, we associate these intervals with number lines, step functions, or specific behaviors of a function in certain domains or ranges.

Given the notation:

- **\((4, \infty)\)** and **\([4, \infty)\)**: This interval represents all numbers greater than 4. The round parenthesis implies that 4 is **not included**, while the square bracket implies 4 is **included**.
- **\((-\infty, 4]\)** and **\((-\infty, 4)\)**: These intervals represent all numbers less than 4. Again, the round parenthesis excludes 4, while the square bracket includes 4.

### Here is a breakdown:

- **\((4, \infty)\)**: All values greater than 4, but not including 4.
- **\([4, \infty)\)**: All values greater than or equal to 4.
- **\((-\infty, 4]\)**: All values less than or equal to 4.
- **\((-\infty, 4)\)**: All values strictly less than 4.

If the graph represents a function that is defined for values **greater than 4** but not including 4, the correct answer would be **\((4, \infty)\)**.

If the graph includes the point at 4 and extends infinitely to the right, the correct answer would be **[4, ∞)**.

If the graph represents all values **less than or equal to 4**, then **(-∞, 4]** is the correct choice.

Without the actual graph, this is the interpretation based on the intervals provided. Could you clarify or provide the graph for a more specific answer?

---

### Related Questions:

1. What does the inclusion or exclusion of endpoints in an interval mean graphically?
2. How can intervals be represented on a number line?
3. How do inequalities relate to intervals on graphs?
4. What are open and closed intervals, and how do they differ?
5. How do we interpret intervals in the context of function domains?

### Tip:
Always check whether the interval includes or excludes boundary points by looking for square brackets \([ ]\) or round parentheses \(( )\).

Which of the following choices corresponds to the graph?

0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
(4, ∞)
(4, ∞)
(-∞, 4]
(-∞, 4]
[4, ∞)
[4, ∞)
(-∞, 4)
(-∞, 4)

Learn how to identify the correct interval or inequality for a graph using interval notation. This problem covers key concepts such as open and closed intervals, inequalities, and number line representation. Suitable for students in Grades 8-10.

Math Problem Statement

( − ∞ , 4 ] (

( − ∞ , 4 ) (

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