Question

Determine if the endpoints for the following piecewise function are opened or closed

-3 x < 2
{2 x ≤ x < 4
5 x ≥ 4

(Answers)

4,2
4,5
2,2
2, -3

Answer 1

In the given piecewise function:

- For \( x < 2 \), the function takes the value -3.
- For \( 2 \leq x < 4 \), the function takes the value 2.
- For \( x \geq 4 \), the function takes the value 5.

Now, let's analyze the endpoints:

1. **For \( x < 2 \)**, the endpoint at \( x = 2 \) is not included (it's an open interval on the left side), so we denote that endpoint as **open**.

2. **For \( 2 \leq x < 4 \)**, the endpoint at \( x = 2 \) is included (it's a closed interval on the left side) and the endpoint at \( x = 4 \) is not included (it's an open interval on the right side). So, \( x = 2 \) is **closed** and \( x = 4 \) is **open**.

3. **For \( x \geq 4 \)**, the endpoint at \( x = 4 \) is included (it's a closed interval on the left side) but we've already noted that in the previous interval it was treated as open.

Thus, summarizing:

- The endpoint at \( x = 2 \) is **closed**.
- The endpoint at \( x = 4 \) is **closed** but treated as open due to the different interval definitions earlier.

Therefore, the correct notation for endpoints is:

- \( x = 2 \) (closed)
- \( x = 4 \) (open)

Given the options and focusing specifically on closed and open practices (with the first appearing intervals):

The answer is **(2, 4)** where \( 2 \) is closed and \( 4 \) is open, matching the situation precisely with the patterns considered.

The endpoints you would write are:

- \( 2 \) is closed: \( [2 \)
- \( 4 \) is open: \( 4) \)

So the correct pairing from your answers is **\( 2, 2 \)** denoting that the value at \( 2 \) has a point. The pairing yields:
- The inclusion at \( 2 \) seen as **closed \([2]\)**
- The value at \( 4 \) treated open (disregard its value in function previous intervals).

Thus the pairs coordinates yielding open/closed status denote:
**2, 2 or also upon refining down could indicate restrictions set \( 4,5 \)** if applied correctly.

To summarize considering pointed confines ** answer is ** (2,2) and also consider \( (4,\) being open indicating alternate options being true.