The problem shown in the image asks to identify each interval as open or closed. The intervals listed are:

1. $(1, 4)$
2. $(- \infty, 7)$
3. $[1, 4]$
4. $[- \infty, 7)$
5. $(0, \infty)$

Here’s the classification of each interval:

1. $(1, 4)$ — This is an open interval because both endpoints are not included.
2. $(- \infty, 7)$ — This is an open interval because infinity is always open, and the 7 is not included (due to the round parenthesis).
3. $[1, 4]$ — This is a closed interval because both endpoints (1 and 4) are included, indicated by square brackets.
4. $[- \infty, 7)$ — This is a half-open interval (or half-closed) because infinity is always open, but 7 is not included.
5. $(0, \infty)$ — This is an open interval because neither endpoint (0 nor infinity) is included.

Would you like more details or explanations on open and closed intervals?

Here are 5 related questions to extend your understanding:

1. What is the difference between an open and closed interval in terms of set notation?
2. How are intervals used in calculus, particularly in defining limits?
3. Can an interval be neither open nor closed? What is such an interval called?
4. How does interval notation help when solving inequalities?
5. What happens to the concept of intervals when considering functions that approach infinity?

Tip: Always remember that parentheses represent openness (not included) and brackets represent closedness (included) when interpreting intervals.