If f(x) is a greatest integer function, then f(-2. 5) is equal to

Options

A. `-3`
B. `-2`
C. 2
D. 3

Answer

To solve the problem, we need to find the value of the greatest integer function, denoted as \( f(x) \), at \( x = -2.5 \).

### Step-by-Step Solution:

1. **Understanding the Greatest Integer Function**:
The greatest integer function, often denoted as \( \lfloor x \rfloor \), gives the largest integer that is less than or equal to \( x \).

2. **Identifying the Value**:
We need to evaluate \( f(-2.5) \), which is equivalent to finding \( \lfloor -2.5 \rfloor \).

3. **Locating -2.5 on the Number Line**:
On the number line, -2.5 lies between -3 and -2. Specifically:
\[ -3 < -2.5 < -2 \]

4. **Finding the Greatest Integer**:
The greatest integer that is less than -2.5 is -3. Therefore, we have:
\[ \lfloor -2.5 \rfloor = -3 \]

5. **Conclusion**:
Thus, \( f(-2.5) = -3 \).

### Final Answer:
\[ f(-2.5) = -3 \]